Multiple Criteria Decision Making in Application Layer Networks

Bayreuther Arbeitspapiere zur Wirtschaftsinformatik Lehrstuhl für Wirtschaftsinformatik Information Systems Management Bayreuth Reports on Information Systems Management No. 36 July 2008 Frank Schneider Multiple Criteria Decision Making in Application Layer Networks ISSN 1864-9300 Die Arbeitspapiere des Lehrstuhls für Wirtschaftsinformatik dienen der Darstellung vorläufiger Ergebnisse, die i. d. R. noch für spätere Veröffentlichungen überarbeitet werden. Die Autoren sind deshalb für kritische Hinweise dankbar. The Bayreuth Reports on Information Systems Management comprise preliminary results which will usually be revised for subsequent publications. Critical comments would be appreciated by the authors. Alle Rechte vorbehalten. Insbesondere die der Übersetzung, des Nachdruckes, des Vortrags, der Entnahme von Abbildungen und Tabellen – auch bei nur auszugsweiser Verwertung. All rights reserved. No part of this report may be reproduced by any means, or translated. Authors: Information Systems and Management Working Paper Series Edited by: Prof. Dr. Torsten Eymann Managing Assistant and Contact: Raimund Matros Universität Bayreuth Lehrstuhl für Wirtschaftsinformatik (BWL VII) Prof. Dr. Torsten Eymann Universitätsstrasse 30 95447 Bayreuth Germany Email: [email protected] ISSN Frank Schneider (University of Bayreuth) 1864-9300 i Contents Contents............................................................................................. i List of Figures ...................................................................................iv List of Tables.....................................................................................vi List of Abbreviations ........................................................................vii List of Symbols..................................................................................ix 1 Introduction ................................................................................ 1 1.1 Starting Position: Trust in eCommerce ............................................. 1 1.2 Objectives of this Study......................................................................2 1.3 Conduct of this Study .........................................................................3 2 Interactions in Application Layer Networks .................................5 2.1 Depicting the Environment................................................................5 2.2 Coordination in Application Layer Networks....................................5 2.2.1 Application Layer Networks...............................................................5 2.2.2 Catallactic Information Systems........................................................6 2.3 Software Agents in Multi Agent Systems...........................................7 2.3.1 Software Agents..................................................................................7 2.3.2 Multi Agent Systems.........................................................................10 2.3.3 Disseminating and Gathering Information ......................................11 2.4 The Object of Interaction: Trading Goods....................................... 12 2.4.1 Homogeneous and Heterogeneous Goods and Services .................12 2.4.2 Price Formation Mechanisms .......................................................... 13 2.5 Differentiation through Reputation................................................. 17 2.5.1 Reputation and Image...................................................................... 17 2.5.2 Reputation Systems..........................................................................18 ii 2.6 Decision Making...............................................................................23 2.6.1 Theory of Decision............................................................................23 2.6.2 The Classical Model for Decision Making........................................25 2.6.3 Multiple Criteria Decision Making.................................................. 28 2.6.4 Preference Modeling through Utility and Values ............................29 3 Multiple Criteria Decision Making ............................................. 31 3.1 Classification of MCDM Methods .................................................... 31 3.2 On Data and Weights .......................................................................32 3.2.1 Scales of Data....................................................................................32 3.2.2 Normalization Techniques for Equalizing Diverse Scales...............34 3.2.3 Weights as Means for Relative Importance of Criteria ...................35 3.3 Multiple Attribute Decision Making ............................................... 38 3.3.1 A Taxonomy of MADM Methods .................................................... 38 3.3.2 Deciding without Preference Information.......................................39 3.3.3 Satisficing (Conjunctive and Disjunctive Approaches) ...................41 3.3.4 Sequential Elimination.....................................................................42 3.3.5 Value Function Methods ..................................................................44 3.4 Multiple Objective Decision Making................................................55 3.4.1 Overview of MODM Methods ..........................................................55 3.4.2 Goal Programming ...........................................................................56 3.5 Decision Aids....................................................................................59 3.5.1 Outranking Relations .......................................................................59 3.5.2 The ELECTRE Approach................................................................. 60 4 Application of the Extended TOPSIS to the Scenario ..................64 4.1 Structure...........................................................................................64 iii 4.2 A Synthesis of ALN and MCDM.......................................................64 4.2.1 Summary of Environment Characteristics ......................................64 4.2.2 Comparison of MCDM Methods ......................................................67 4.2.3 Conclusion for Method Application................................................. 71 4.3 Scenario Specifications.....................................................................72 4.3.1 Environment and Actors ..................................................................72 4.3.2 Interaction between Actors ..............................................................73 4.3.3 Offer Attributes.................................................................................75 4.3.4 Principal’s Preference Information..................................................76 4.4 The Extended TOPSIS......................................................................77 4.4.1 Description of the Technique...........................................................77 4.4.2 Application of the xTOPSIS: A Numerical Example........................78 4.5 Findings from the Scenario Application ......................................... 83 4.5.1 Intertemporal Comparison of Reached Agreements...................... 83 4.5.2 Seller Evaluation ............................................................................. 84 4.5.3 Summary ......................................................................................... 84 5 Conclusion .................................................................................85 5.1 Results ..............................................................................................85 5.2 Suggestions for Research and some Critical Annotations.............. 88 References ...................................................................................... 90 Appendix........................................................................................ 105 Appendix A........................................................................................................105 Appendix B: Case Study....................................................................................108 iv List of Figures Figure 1: Percentage of EU enterprises' total turnover from eCommerce via Internet ....1 Figure 2: General approach of this work........................................................................ 4 Figure 3: Outline of the 2nd Section................................................................................ 5 Figure 4: The ALN as a virtual hard disk ....................................................................... 6 Figure 5: The Procedural Reasoning System ................................................................. 9 Figure 6: Typology of goods ..........................................................................................13 Figure 7: Price formation mechanisms .........................................................................14 Figure 8: Well-known auction types .............................................................................16 Figure 9: Building blocks of reputation ....................................................................... 18 Figure 10: Calculation of trust in ReGreT.................................................................... 22 Figure 11: Decision-making process............................................................................. 24 Figure 12: Non-sequential decision-making process................................................... 25 Figure 13: Subprocess of defining a decision matrix ................................................... 26 Figure 14: Classical model of decision-making............................................................28 Figure 15: MCDM methodology ....................................................................................31 Figure 16: Outline of the 3rd Section............................................................................. 32 Figure 17: Relative and cumulative weights in value trees .......................................... 37 Figure 18: The subprocess of defining weights ............................................................38 Figure 19: Overview of MADM methods...................................................................... 39 Figure 20: Efficient frontier .........................................................................................40 Figure 21: Process of the Simple Additive Weighting method ....................................46 Figure 22: Process of the Weighted Product Method ..................................................48 Figure 23: Generic fourand five-level hierarchies .....................................................49 Figure 24: Simplified process of the Analytic Hierarchy Process................................50 v Figure 25: A three-level hierarchy for means of travel .................................................51 Figure 26: Euclidean distances to the ideal solutions in two-dimensional space....... 52 Figure 27: Process of the Technique for Order Preference by Similarity to Ideal Solution . 53 Figure 28: A taxonomy of methods for Multiple Objective Decision Making............. 56 Figure 29: Portray of feasible solutions in a GP example............................................ 57 Figure 31: Outline of the 4th Section............................................................................. 64 Figure 32: The main process of buying storage capacity and the MCDM blackbox ...66 Figure 33: Prerequisites for the appropriate MCDM method .....................................68 Figure 34: Classification of MCDM methods in the light of the scenario ....................71 Figure 35: Scheme of the scenario ............................................................................... 73 Figure 36: Interaction within the ALN......................................................................... 74 Figure 37: Process of the extended TOPSIS..................................................................77 vi List of Tables Table 1: Standard cases for the employment of DBAs ................................................. 10 Table 2: Distinction between DPS and MAS.................................................................11 Table 3: Example of a decision matrix .........................................................................26 Table 4: Terminology in decision-making ................................................................... 27 Table 5: Example of a multiple criteria decision problem...........................................28 Table 6: Scale levels and their properties..................................................................... 33 Table 7: Normalization with linear scale transformation............................................ 34 Table 8: Vector normalization...................................................................................... 35 Table 9: Maximin and Maximax decision rules............................................................41 Table 10: Satisficing approaches ..................................................................................42 Table 11: Additive and multiplicative weighting approaches ...................................... 47 Table 12: Assembling positive and negative ideal solutions........................................ 53 Table 13: Outranking relations..................................................................................... 59 Table 14: Summary of scenario characteristics............................................................ 65 Table 15: Dimensions of the comparison table ............................................................69 Table 16: Comparison of MCDM methods................................................................... 70 Table 17: Offer attributes.............................................................................................. 75 Table 18: Weight vector................................................................................................ 76 Table 19: Decision matrix of the 1st round ................................................................... 79 Table 20: Weighted normalized decision matrix of the 1st round ............................... 79 Table 21: Closeness values and ranking for the 1st round ............................................80 Table 22: Decision matrix of the 2nd round.................................................................. 81 Table 23: Weighted normalized matrix, closeness values and ranks of the 2nd round... 82 Table 24: Weighted normalized matrix, closeness values and ranks of the 3rd round... 82 vii List of Abbreviations AHP.................................................................................... Analytical Hierarchy Process ALN ....................................................................................... Application Layer Network BDI.............................................................................................. Belief-Desire-Intention CAGR ............................................................................Compound Annual Growth Rate CIS...................................................................................Catallactic Information System DBA...............................................................................................Digital Business Agent DM ...........................................................................................................decision-maker DPS......................................................................................Distributed Problem Solving EbA...............................................................................................Elimination by Aspects ELECTRE................................................... ELimination Et Choix Traduisant la REalité eRep ..........................................Social Knowledge for e-Governance (project acronym) EU .......................................................................................................... European Union EUR........................................................................................................................... Euro Euro NCAP................................................. European New Car Assessment Programme FPSB................................................................................................ first-price sealed-bid g............................................................................................................................ gram(s) GB.........................................................................................................................gigabyte ICT............................................................. information and communication technology IDB................................................................................................ Impressions Database IVD................................................................................................ Ideal Vector Database km ......................................................................................................................kilometer kmph ...................................................................................................kilometer per hour LM.................................................................................................Lexicographic Method LS ............................................................................................. Lexicographic Semiorder Ltr................................................................................................................................liter MAS................................................................................................... Multi Agent System MADM .................................................................... Multiple Attribute Decision Making MCDM........................................................................Multiple Criteria Decision Making MODM ....................................................................Multiple Objective Decision Making ODB...................................................................................................Outcomes Database PD..........................................................................................................Partner Database 4 Section Section Trust in eCommerce Goals of this study The approach Introduction 1. 1. Application Layer Networks Software agents and Multi Agent Systems Trading goods and forming prices Reputation and reputation systems Decision-making – Theory and classical model Interactions in Application Layer Networks 2. 2. Data and weights Multiple Attribute Decision Making Multiple Objective Decision Making Decision Aids Multiple Criteria Decision Making 3. 3. Synthesis of MCDM and ALN Scenario Specifications The TOPSIS extension Findings from the application Applying the MCDM Method 4. 4. Results Suggestions for research and some Critical Words Results & Outlook 5. 5. Figure 2: General approach of this work The Appendix at the end includes the example of a multiple criteria decision problem concerning the purchase of a car. The case study complements the work in terms of illustrating the calculation steps for almost all presented decision-making methods. 5 2 Interactions in Application Layer Networks 2.1 Depicting the Environment This Section clarifies the used terminology and describes the economic environment in which the decision-making scenario is located (Figure 3). To achieve that, we explain the coordination principle (Subsection 2.2) and present the actors (Subsection 2.3). Thereafter, we clarify the rationale for and the conduct of interaction (Subsection 2.4) before we attend to the function of reputation in general and as an inherent institution of the environment (Subsection 2.5). Finally, we explicate decisionmaking and glance at preference modeling (Subsection 2.6). ALN ALN Application Layer Networks Catallactic Information System Application Layer Networks Catallactic Information System 2.2 MAS MAS Software agents Multi Agent Systems Information transmission Software agents Multi Agent Systems Information transmission 2.3 Reputation and image Reputation systems Reputation and image Reputation systems Reputation Reputation 2.5 Goods and Services Price Formation Mechanisms Goods and Services Price Formation Mechanisms Trading Trading 2.4 Theory of decision Classical model of decisionmaking Preference modeling Theory of decision Classical model of decisionmaking Preference modeling Decision Making Decision Making 2.6 Terminology Terminology Subsection ALN ALN Application Layer Networks Catallactic Information System Application Layer Networks Catallactic Information System ALN ALN Application Layer Networks Catallactic Information System Application Layer Networks Catallactic Information System 2.2 MAS MAS Software agents Multi Agent Systems Information transmission Software agents Multi Agent Systems Information transmission MAS MAS Software agents Multi Agent Systems Information transmission Software agents Multi Agent Systems Information transmission 2.3 Reputation and image Reputation systems Reputation and image Reputation systems Reputation Reputation 2.5 Goods and Services Price Formation Mechanisms Goods and Services Price Formation Mechanisms Trading Trading Goods and Services Price Formation Mechanisms Goods and Services Price Formation Mechanisms Trading Trading 2.4 Theory of decision Classical model of decisionmaking Preference modeling Theory of decision Classical model of decisionmaking Preference modeling Decision Making Decision Making 2.6 Terminology Terminology Subsection Figure 3: Outline of the 2nd Section 2.2 Coordination in Application Layer Networks 2.2.1 Application Layer Networks An extensive computer network which provides services requiring a considerable amount of resources is called Application Layer Network (ALN). In order to acquire these resources, ALNs use communication infrastructures such as the Internet in order to interconnect numerous individual computers [ESR+05, 7]. Resource allocation by means of centralized mechanisms proves to be inefficient for two reasons: First, the coordinating institution is supposed to transfer instantly a huge number of requests from connected peers. Second, rapidly changing member 6 structures in dynamic networks and multiple varying environmental states place great demand on the processing capacities of the coordinator. Especially large-scale networks call for coordination mechanisms which are capable of allocating resources and services in real time to fulfill specified service-levels [ERA+04, 10], [Eyma03, 53–54]. Hence, we explain a decentralized philosophy in the next Subsection. A prominent example for an ALN is the Peer-to-Peer system BitTorrent which enables members to share resources and transfer files to each other [SNV+07, 91–92], [Cohe03, 1]. For the application of ALNs in academics, prime examples are the Stanford University’s Folding@home project or the distributed search for extra-terrestrial intelligence, SETI@home, run by the Space Science Laboratory at the University of California, Berkeley [Pand08, 1-2], [Univ08]. In the scenario of this work, the ALN is a virtual hard disk composed of space provided by linked up computer systems (Figure 4). ALN: virtual hard disk ALN: virtual hard disk Computer system with hard disk Computer system with hard disk Figure 4: The ALN as a virtual hard disk 2.2.2 Catallactic Information Systems With regard to the economic principles of Friedrich August von Hayek’s Catallaxy, the Catallactic Information System (CIS) proposes a decentralized coordination mechanism as a new paradigm for the design of information systems [EPSc00, 349– 350]. Hayek’s Catallaxy can be understood as a synonym for free-market economy, using prices as coordination mechanisms and, without knowledge of the individual actors’ 7 behaviors, leading to a “spontaneous order” [Eyma03, 157]. The concept assumes members in the system are self-interested and strive to maximize their utility. As participants can neither foresee future market states nor predict other agents’ behaviors (constitutional ignorance), they are forced to make decisions under bounded rationality [ESR+05, 13]. The CIS molds the concept of Catallaxy using the technology of Multi Agent Systems (MAS), which consist of software agents representing the actors in the Catallaxy (cf. Subsection 2.3.2). The evaluation of a Catallaxy-based coordination mechanism has been subject to research in the CATNETS project. The authors deduced several fields for further research, including, but not limited to, the necessity to implement electronic institutions and social control mechanisms to cope with volatile service qualities and malevolent software agents [StEy07, 27–30]. With respect to these findings we implement a governance mechanism in our future scenario. 2.3 Software Agents in Multi Agent Systems 2.3.1 Software Agents 2.3.1.1 Agents in Computer Science The Merriam-Webster explains the term agent as “one who is authorized to act for or in the place of another”, i.e. a representative of someone or something [Merr08a, § 4]. The translation of the traditional meaning in the context of computer science is called software agent or intelligent agent. Due to the versatility of agents in applications, a definite and overarching explication is still open [Burk03, 1014–1015], [Nwan96, 208]. Referring to Wooldridge, we understand software agents as autonomous entities interacting with their environment in a bidirectional way: Agents receive input through sensors and use effectors to react with output actions [Wool00, 29]. In addition to autonomy, our agents are intelligent in the sense that they are flexible in conducting actions to achieve their goals. Flexibility in turn comprises the following three features:  reactivity refers to immediate response to environmental changes, 8  pro-activeness is the ability to take the initiative, and  social ability means interacting with other agents. Each feature has implications for the remainder of this work: Social ability requires the presence of additional agents to cooperate with as well as the implementation of a common communication language. Pro-activeness and reactivity seem contradictory, and reactivity even puts autonomy into question – in order to balance these features, an internal model is required that allows elaborating and adjusting plans of action [Wool00, 32–33]. Supplementary to Wooldridge’s definition of reactivity, suggestions for further potential dimensions are listed in [Burk03, 951–953]. Nwana takes up learning which evolves from past interactions with the environment, and argues for its explicit consideration [Nwan96, 210]. Learning is “any instance of improvement of behavior through increased information about the environment” [Kael93, 4]. Though learning seems implicit when attributing reactivity to agents, it can take various forms in MAS; a general characterization can be found in [SeWe00, 260–264]. In our context, the agent learns from encounters with others in the way that he adjusts his beliefs about the environment. 2.3.1.2 Practical Reasoning in the Internal Model Between perception and action, the internal model provides the basis on which agents make decisions and fulfill their assigned function. Practical reasoning is the two-phase process of deliberation and means-end reasoning. At first, deliberation refers to deciding what state to achieve, whereas means-end reasoning afterwards refers to deciding how to achieve the particular state. States an agent has committed to are called intentions: they drive means-end reasoning, constrain future deliberation, and exert influence on beliefs [Wool05, 66–69]. Among the available models, we will outline the Procedural Reasoning System (PRS) in the following paragraphs, since it is an approved implementation for deliberate agents and embodies the Belief-Desire-Intention (BDI) paradigm [Wool05, 82]. Farther, the PRS corresponds to the framework used in the eRep project [SPV+07, 13]. In the PRS architecture, four attitudes determine the behavior of the agent, i.e. how practical reasoning is conducted. Our agent is in possession of the key data structures 9 beliefs, desires, intentions and plans (Figure 5) [Wool96, 663–664]:  Belief: knowledge emerging from information about environmental states received and updated through the agent’s sensor. Belief is subjective and not necessarily correct or complete.  Desire: objectives or tasks, the agent is supposed to accomplish, and priorities associated with them. Desire represents the motivational state of an agent.  Intentions: deliberative state. Intentions are the currently chosen course of action, i.e. the objective the agent has committed to pursue at the moment.  Plans: particular patterns of instructions to achieve an objective. Plans are made up of a goal, a context (preconditions) and a body (the sequence of actions to carry out). Data Input Data Input Action Output Action Output Environment Desires Intentions Interpreter PlansBeliefs Sensor Agent Agent Figure 5: The Procedural Reasoning System [Wool05, 83] The process of procedural reasoning works as follows: At the beginning, the interpreter (planner) has beliefs about the world, a collection of plans and a top-level goal. He browses his library of plans to extract those ones that match both goal and precondition of the current state. Afterwards, in the process of deliberation the agent selects a plan from the resulting set of options. A practical means to allow rational justified selections is the implementation of a utility value for options: then the plan 10 with the highest value is selected (for an explication of utility cf. Subsection 2.6.4). After execution of the chosen plan, new goals arise and require deliberation and so on. [Wool05, 83–84]. 2.3.1.3 Digital Business Agents Software agents acting on behalf of a legal entity in commercial environments are called digital business agents (DBA). They are obedient, utilitarian entities whose commercial function (goal) is defined by a principal (human being or organization). Obedience implies that the DBA’s paramount goal is always aligned with the principal’s one: to act in the owner’s interest. This in turn justifies the utilitarian attitude of the agent, expressed by rational conduct in order to contribute to the principal’s utility [Eyma03, 24–26]. Roughly, one may distinguish between two different cases in which DBAs are used: the cooperative and the competitive environment (Table 1). Table 1: Standard cases for the employment of DBAs (based on [Eyma03, 27]) Paradigm Cooperation Competition Pursued Goals Common Collective utility maximization (e.g. low cycle time) Conflicting Individual utility maximization (e.g. high profit) Environment Closed system Number of participants is constant Open system Agents enter and leave the system during runtime Number of agents per principal Multiple One Example Product design Procurement This work assumes a competitive environment, since this corresponds with the CIS underlying the ALN and the research subject of the eRep project. At present, possible purposes of DBAs include capacity management, supply chain coordination, product design, and trade on electronic marketplaces [Eyma03, 99–107]. This work will focus on the decision-making process of DBAs trading on an electronic marketplace. 2.3.2 Multi Agent Systems Discussing how various agents interact with each other involves explaining how coordination is realized between them. On the one hand we have cooperation through 11 Distributed Problem Solving (DPS), on the other hand competition is solved through negotiation processes (Table 2) [HuSt00, 83]. While in DPS a common goal is fractured top-down and solved bottom-up, MAS have the top goal emerging from the bottom as a result of the various agents’ competing goals [Eyma03, 49–51]. Table 2: Distinction between DPS and MAS [RoZl98, 15–16] DPS MAS System designing Centralized Decentralized Coordination Paradigm Cooperation: Agents cooperate to achieve the common goals Competition: Agents negotiate with each other Pursued Goals Common Conflicting In accordance with the concept of DBAs, participating agents in MAS are rational, self-interested and utility-maximizing; they strive to realize the interest of their respective owner [RoZl94, 31]. Thus, DBAs negotiate with each other in order to achieve their goals. As mentioned before (cf. Section 2.2.2), the implementation of the CIS constitutes a price mechanism to encourage coordination between the rival agents. Assuming that we apply the MAS idea to an electronic marketplace, we predict the overarching goal is system efficiency in terms of a Pareto efficient allocation of traded goods with their respective utility (welfare maximization) [Vari06, 618–620], [RoZl94, 31]. 2.3.3 Disseminating and Gathering Information With the implementation of reputation (cf. Subsection 2.5.1.2), it becomes necessary to compute an aggregate which reflects the common image of the target agent. We assume agents disseminate their experiences on a voluntary basis, though this contradicts with the definition of the self-centered, utilitarian agent (cf. Subsection 2.3.1.3). Miller et al. suggest a complex reward system based on scoring rules to elicit honest feedback from other participants [MRZe05]. For the sake of simplicity, we suppose agents spread information on a voluntary basis. In order to allow dissemination and accumulation of information in the ALN, a formal communication mechanism has to be implemented. Possible forms range from broadcasting mechanisms over blackboard systems to direct communication 12 [Eyma03, 56–58]. Whereas broadcasting means transmitting information to all participants (“one-to-many”), direct communication relates to the opposite channel-wise messaging (“one-to-one”). Blackboard systems store news (feedback) in repositories and disseminate information upon request; well-known eCommerce examples include online reputation systems such as the ones of Amazon Marketplace, Ebay, or Yahoo!Shopping [Amaz08], [Ebay08a], [Yaho08]. Researchers of the eRep project have also examined possible means of communication and their effects on reputation [CoPa07, 9–13]. Despite the high degree of decentralization of our reference system, we presume agents store data partially in public local repositories which are accessible for all connected members when requesting information (Subsection 2.5.2.3). 2.4 The Object of Interaction: Trading Goods 2.4.1 Homogeneous and Heterogeneous Goods and Services In ordinary language, goods are “something that has economic utility or satisfies an economic want“ [Merr08b]. Moreover, we need to differentiate goods with respect to their impact on marketing: While some goods do not allow differentiation and further market segmentation, some goods permit multi-dimensional customization. Thus, the following terminology is being used from now on: When we talk about goods, we mean goods and services. Very complex, multi-faceted goods which can hardly be compared are named heterogeneous goods (e.g. cars, advisory, holiday trips), while very simple goods, which only differ in their price, are called homogeneous goods (e.g. power, coal or storage capacity in megabytes) [WRSc05, 69], [GLFo04, 257]. These two types of goods can be understood as extreme values on a continuum – many goods are positioned in between. To determine the grade of complexity, we use the typology of Woratschek and classify goods on three dimensions: behavioral uncertainty associated with the transaction, the degree of customer integration and the degree of customization [WRSc05, 69], [Wora96, 69]. We can illustrate the continuum between homogeneity and heterogeneity using a sliced cube (Figure 6). A distinction between homogeneous and heterogeneous goods is applicable in ALNs as well: the former are termed resources, the latter services. Moreover we assume application services (e.g. converting a Portable Document Format file [PDF]) can be broken down into resources needed to provide the service (like hard disk capacity and 13 processing power) [StEy07, 7–8]. We hold on to a commodity or plain resource (such as a coal or wheat) and assume sellers cannot modify the good in a way that allows them to differentiate from competing suppliers. From a customer’s perspective, all offers are equal except for the price and the potential supplier (uncertainty about the suppliers’ trustworthiness is a distinguishing feature). low high Behavioral uncertainty lowhigh Customer integration low high Customization Heterogeneous goods Homogeneous goods Advisory Car (mass-customized) Storage capacity low high Behavioral uncertainty low high low high Behavioral uncertainty lowhigh lowhigh Customer integration low high Customization low high low high Customization Heterogeneous goods Homogeneous goods Advisory Car (mass-customized) Storage capacity Figure 6: Typology of goods (based on [Wora96, 69]) The particular object of trade in the scenario of this work is storage capacity in units of one gigabyte per month (GB/month). 2.4.2 Price Formation Mechanisms 2.4.2.1 How Prices Emerge The price demanded by producers represents the evaluation of a product in monetary units. From a customer’s point of view, the price is a sacrifice made to benefit from the possession of something, i.e. his willingness-to-pay depends on his associated utility with the particular good [Simo92, 3–4]. From the producer’s position, the price has to compensate for costs incurred in the manufacturing process and has to 20 As intuitively assumed and supported by the findings of a lab experiment in 2004, the gain from one’s own experience is likely to exceed a cumulative public reputation value [BKOc04, 1595]. These findings are underpinned by recent survey results showing 60 percent of private online shoppers remain loyal to vendors they had a positive shopping experience with [Niel08, 5]. Since the effects of locally managed reputation are investigated in the eRep project, the following paragraphs focus on such reputation systems. 2.5.2.2 A Panoramic View on Current Systems It is beneficial for the development of an appropriate reputation framework to contrast outcomes from empirical research with theoretical findings [Dell03]. A valuable roundup of reputation systems serves three purposes: it lists existent frameworks, describes the designs, and extracts particular contributions from each system. Sabater and Sierra provide such a summary: they reviewed thirteen different concepts and classified them on seven dimensions (cf. Appendix A 2, p. 106, and for the abbreviations Appendix A 1, p. 105) [SaSi05, 55–56]. We explain two of these dimensions, since they exert direct influence on the selection of decision-making tools. First, information sources comprise the types of sources taken into account when determining the reputation value of another entity. The perceived reputation of a trader depends on the subjective image of the customer built from impressions and the trader’s circulating social reputation. The subjective impressions stem from experiences made in direct interactions or observations with the trader. Following the narrow definition above, witnesses’ experiences are aggregated and result in social reputation. Beyond these experiences, information based on the trader’s societal affiliations and social relations is likely to influence his picture. Hence, those potential sources are as well subsumed under social reputation [SaSi05, 35–37]. Second, an associated reliability measure helps to understand how stable each impression is. Thus, our customer can use the measure to weight the information value. In communities with a tremendous number of entities, the reliability measure serves as a threshold and filters less credible impressions. But even the subjective image a customer has is instable: Memories are fugacious, and in the course of time experiences blur or disappear completely. By assigning a reliability measure to each impres- 21 sion, the individual computation of an aggregate reputation score becomes more precise and comprehensible [SaSi05, 40–41]. Our scenario with autonomous and deliberate agents encourages local decisionmaking. Hence, a reputation system that makes use of direct experience as well as witness information has to be implemented. Though not critical, a measure for reliability is useful when dealing with large-scale MAS. With the aid of Sabater and Sierra’s comparison, two possible systems are identified: AFRAS and ReGreT. Since ReGreT includes a comprehensive framework for evaluating sociological information, we prefer it to AFRAS and present it in the following chapter. 2.5.2.3 ReGreT The ReGreT system consists of a direct trust and a reputation module to assess the trustworthiness (trust) of a prospective, so called target agent. Trust towards a target agent is the weighted sum of social reputation and direct trust (i.e. image). The computation of each component is determined by the system’s architecture: it distinguishes between three reputation dimensions, the individual dimension, the social dimension and the ontological dimension (Figure 2 1) [SaSi01, 194]. In the next paragraphs, each dimension with its components will be presented in a nutshell; for a detailed explication see [Saba03, 44–62]. On the individual level, outcomes of dialogues between agents are used to compute a direct trust value. An outcome is represented by a subjective rating and a tuple of information; it is stored in the outcomes database (ODB). The tuple of information characterizes the outcome (e.g. price or expected quality) and the rating reflects the perceived evaluation. Direct trust is usually the most stable source to predict the sincereness of a partner; on the downside, it is unavailable for new entrants and expensive to build [Saba03, 44–46]. In the social dimension, the reputation measure is computed by the weighted results of three sources: witness, neighborhood, and system reputation. The weights are obtained from the credibility of each source, which is in turn calculated from the numbers of impressions and the standard deviations [SaSi01, 195]. We talk about witness reputation when information is collected from other agents who transmit their direct experiences or feedback obtained from peers. Evaluated 22 impressions of witnessed outcomes are recorded in a second storage, the impression database (IDB). Neighborhood reputation is determined by the target’s social environment and the relations the target has established with his environment. It is comparable to prejudice, but not necessarily discriminating. System reputation is based on the target’s role in a group. It assumes that roles adhere to certain observable features or behaviors which may be assigned to the target agent [Saba03, 47–48]. Trust of Agent A Interaction AB Impression Impression Social Reputation SDB SDB ODB ODB IDB IDB Social Relation Group Outcome Direct trust ! ! Social Dimension Individual Dimension Neighbourhood reputation System reputation Witness reputation Trust of Agent A Interaction AB Interaction AB Impression Impression Social Reputation SDB SDB ODB ODB IDB IDB Social Relation GroupGroup Outcome Direct trust ! ! Direct trust ! !! ! Social Dimension Individual Dimension Neighbourhood reputation System reputation Witness reputation Figure 10: Calculation of trust in ReGreT (based on [Saba03, 92]) The computation of neighborhood and system reputation depends on the group the individual belongs to; thus, both can be understood as group knowledge, and both are influenced by the social structures. Those structures, mapped as sociograms, are stored in a third container, the sociogram database (SDB). Though not fully specified yet, sociograms will support each estimate of credibility for all considered impressions by providing aid for proper weight assessment (e.g. witness reputation issued 23 by a node related to the target agent may be biased and thus less valuable than others’ feedback) [Saba03, 51], [Saba03, 41]. Finally, the ontological dimension describes the context of information on which the target agent is rated. The ODB does not merely provide an aggregated value on each outcome but also detailed information on attributes such as price or delivery date; our subject can evaluate the overall impression by combining different aspects according to his preferential structure. This reflects different perceptions in real life, in which the seller’s reputation strongly depends on the rating customer [Saba03, 61]. König et al. propose a completely decentralized implementation of the ReGreT system using peer-to-peer technology for information exchange [KKWi07]. Due to its complexity, we reject their suggestion and presume the IDB is centrally implemented and social reputation of an agent is identically perceived by all participants. Of course, this does not affect the decentrally calculated image estimate. We assume our participants will consider potential partners’ social reputation as well as direct trust from previous encounters. Consequently, social reputation and image are differentiating features for agents in MAS. 2.6 Decision Making 2.6.1 Theory of Decision Decision theory is concerned with a decision-maker’s (DM) goal-directed rational behavior of coming to a decision in presence of possible options. Rationality implies deliberating about the action before and during decision-making, as well as commitment to the selection [SzWi74, 3–5]. In this work agents undertake decision-making and serve as proxies for their principal, the DM. A distinction is made between normative and descriptive decision theory: Normative decision theory prescribes how problems can be solved. It provides advice on problem solving by formal means of depicting initial situations and solutions. In contrast, descriptive decision theory researches empirical findings and deals with the ex post analysis of decisions made [Laux07, 2], [SzWi74, 18–21]. Decision-making is a multi-stage process that “begins with the identification of a stimulus for action and ends with a specific commitment to action” [MRTh76, 246]. 24 The famous economist and Nobel prize winner Herbert A. Simon (1960) proposed a sequential model with the three principal phases intelligence, design, and choice – similar in structure and content to the models later developed by Irle (1971) or Szyperski (1974) (Figure 11) [Simo77, 40], [SzWi74, 7–10]. The first phase, intelligence, covers the search for decision predicates in the environment; Simon has baptized this phase in analogy to the military meaning. The following step, design, involves forging, developing, and studying possible conduct. Finally, the choice activity deals with selecting a particular conduct from the available ones [Simo77, 40–41]. Intelligence Design Choice Review Simon Problem detection Info search Option creation Evaluation Ranking Decision CheckupIrle Szyperski Cognition Conception Realization Development Mintzberg et al. Identification Selection CyclesSequence Intelligence Design Choice Review Simon Problem detection Info search Option creation Evaluation Ranking Decision CheckupIrle Szyperski Cognition Conception Realization Development Mintzberg et al. Identification Selection CyclesCyclesSequence Sequence Figure 11: Decision-making process (cf. [SzWi74, 7–10], [Simo77, 40–41]) Later on, Mintzberg et al. (1976) recommend a non-sequential, iterative model with three intertwined phases comprising of seven central routines (Figure 12) [MRTh76, 252]. In contrast to the sequential models, their proposal assumes rather an iterative process of routines than the linear succession of actions. Iterations include cycles between routines within a phase as well as cycles between phases. The initial phase is termed identification and comprises two routines. The first, decision recognition, is concerned with the identification of problems, crises, and opportunities. The second routine, diagnosis, deals with accumulation and assessment of related information, and determination of cause-effect relationships [MRTh76, 253– 254]. The development stage is composed of the search and the design routine. While the search aims at finding existing solutions, design is about the development of custommade solutions as well as the modification of ready-made ones. The purpose of both 25 routines is defining options for later decision [MRTh76, 255–256]. 6 Evaluationchoice Evaluationchoice Screen Screen Authorization Authorization Design Design Search Search Diagnosis Diagnosis Decision recognition Decision recognition SelectionDevelopmentIdentification 12 3 4 5 7 6 Evaluationchoice Evaluationchoice Screen Screen Authorization Authorization Design Design Search Search Diagnosis Diagnosis Decision recognition Decision recognition SelectionSelectionDevelopmentDevelopmentIdentification Identification 12 33 44 55 7 Figure 12: Non-sequential decision-making process [MRTh76, 266] Finally, during the selection stage, three routines take place: The screen routine is concerned with the elimination of infeasible alternatives. In the evaluation-choice routine possible courses of action are evaluated and a choice is made. The last routine, authorization, deals with the submission of the decision to superior instances for approval [MRTh76, 257–260]. Depending on the model, the focus for this work lies on the choice stage (Figure 11) or the selection stage (Figure 12), both dealing with formal models for comparing and ranking considered alternatives. 2.6.2 The Classical Model for Decision Making Whether we approve of Simon’s sequential decision process or the cycling phases of Mintzberg et al., decision-making is concerned with selecting one or more options from a number of alternatives. In order to support DMs, decision matrices are commonly used to visualize and formulate decision situations [Laux07, 36–37], [YoHw95, 3]: The columns in the matrix represent the criteria and the rows the alternatives with their specific outcome vector. 26 We show an example situation below: A passenger who is requested to journey lowbudget from Frankfurt to Munich is confronted with three travel options (Table 3). Table 3: Example of a decision matrix Criterion Alternative C1: Costs incurred A1: Take the train EUR 70 A2: Take the car EUR 120 A3: Travel by airplane EUR 150 A decision matrix is constructed by gathering and attributing information to alternatives and criteria (Figure 13; processes in this work are illustrated using activity diagrams of the UML notation, see [OMG08]). Determine outcomes aij Determine outcomes aij Identify n alternatives Identify n alternatives Identify m attributes Identify m attributes Decision matrix Decision matrix Define decision matrix Define decision matrix Define decision matrix Data Data Determine outcomes aij Determine outcomes aij Identify n alternatives Identify n alternatives Identify m attributes Identify m attributes Identify n alternatives Identify n alternatives Identify m attributes Identify m attributes Decision matrix Decision matrix Define decision matrix Define decision matrix Define decision matrix Define decision matrix Define decision matrix Define decision matrix Define decision matrix Data Data Figure 13: Subprocess of defining a decision matrix A decision matrix is a particular decision model with some building blocks which are always apparent (Table 4) [Laux07, 19–26]. We denote by the decision matrix A on the whole × \nm , the set of n alternatives {} =!, 1, , i AAi n, the set of m criteria {} , 1, , j CC j m=…. Upon deciding, our passenger picks A1 and faces the safe outcome a11= 70, i.e. paying 70 Euros for the train ticket. 27 Table 4: Terminology in decision-making [Laux07, 19–26] Term Description Symbol Example A goal describes an aspired situation or change of present state. It is formulated using a preference function and the criterion to optimize. Goal The preference function (which represents the DM’s preference structure) evaluates outcomes. = (Ai) Travel cheaply from Frankfurt to Munich (one-way) Alternative An alternative is a unique option characterized by a specific outcome. At least two alternatives are necessary to require decision-making. Ai A1: Take the train A2: Take the car A3: Travel by airplane Outcome An outcome is a vector of values representing a unique combination of goal-relevant criteria of an alternative. The vector has to be unique to distinguish his respective alternative from others. aij a 1j: (Costs: EUR 70) a2j: (Costs: EUR 120) a3j: (Costs: EUR 150) Criteria Criteria are parameter values for goals (e.g. costs, duration). Cj C 1: Cost C2: Duration State (environmental) Environmental states depend on exogenous parameters which influence decision-making. A state consists of influencers, i.e. data that changes the parameter values of outcomes and thereby the evaluation of alternatives. States can either be uncertain or definite; whereas the latter simplifies decision-making (values of outcomes are scalar and no inherent vectors), uncertainty involves risk estimation. Instable gas price, new outcome vector for alternative two: a2j(low gas price): (Costs: EUR 95) a2j (normal gas price): (Costs: EUR 120) a2j (high gas price): (Costs: EUR 140) The relationship between these building blocks in the classical model of decisionmaking is depicted below (Figure 14): We see the outcome depends on the interplay of decision and current state. With respect to brevity, we disregard uncertainty and environmental states here. This in turn leads to the following simplification: () () () () ( ) () () () i i ii ii AauauA AuA  = The calculated preference value  of an alternative Ai is equal to the utility ui of the outcome ai [Laux07, 27]. 28 Preference function Preference function Goals Goals Outcomes Outcomes States States Specifc State Specifc State ? ? ? ? ? ? Decision Decision Alternatives Alternatives Preference function Preference function Goals Goals Outcomes Outcomes States States Specifc State Specifc State ? ? ? ? ? ? Decision Decision Alternatives Alternatives Decision Decision Alternatives Alternatives Figure 14: Classical model of decision-making (based on [ZiGu91, 3]) Thus, when we know the preference value for all alternatives, an utility-maximizing decision can be made without explicitly deriving utility from each parameter value. The question is whether all alternatives with their respective outcomes are available or not. Returning to the example (cf. Table 3), we recommend taking the train, which dominates the other alternatives in minimizing costs. 2.6.3 Multiple Criteria Decision Making Under certainty, classical models can cope with decision-making as long as the preference function draws a comparable value out of each alternative. Everyday problems are usually more demanding: A comprehensive judgment involves balancing multiple goal-related criteria which are often competing [BeSt02, 1]. This challenge is called aggregation problem [Roy05, 14]. The modified decision matrix (Table 5) from the previous Subsection adds the criterion “travel time” to the problem. Table 5: Example of a multiple criteria decision problem Criteria Alternative x1: Costs incurred x2: Travel time A1: Take the train EUR 70 4 hrs. A2: Take the car EUR 120 3.5 hrs. A3: Travel by airplane EUR 150 2.5 hrs. 29 Although this problem seems simple, the challenge lies in managing the trade-off between travel time and costs (assuming less travel time is associated with a higher utility). Time and costs are incommensurable units (What is the value of an hour in Euros? How much time can I buy for a certain amount of money?) and no alternative dominates the others on both dimension (the train is now less attractive due to the long travel time). We are concerned with Multiple Criteria Decision Making (MCDM) when we take account of multiple conflicting criteria which need to be balanced [BeSt02, 5]. In our later scenario, the buying agent is choosing between several sellers, which differ in social reputation, image and the demanded price. While shoppers seek concurrently a high reputation and a low price, well-reputed sellers will likely seize their good name and ask for a premium (cf. the results of the experiment in [RZSL06, 21]). 2.6.4 Preference Modeling through Utility and Values The predictability of the environmental states influences the means of preference modeling and distinguishes between preference representations under certainty and under risk. When we deal with uncertainty or risk, we refer to a preference representation function as a utility function, and when all states are certain, we refer to a preference representation function as a value function [Dyer05, 267–268], [BeSt02, 95], [KeRa93, 15–16]. In sympathy with Dyer et al. we exclude the field of Multiattribute Utility Theory here and assume value functions are either implicit or no such function exists at all [DFS+92, 647]. And since we also omitted cases of uncertainty and risk, we do not need to pay attention to utility functions from now on (for details on utility see [Vari06, 54–56]). Instead, we define value as being proportional to utility, i.e. a higher value implies always a higher utility (i.e. monotonically increasing). In case outcome and evaluation are positively correlated, we deal with a benefit attribute (i.e. maximization goal), in case they correlate negatively, a cost attribute is considered (i.e. minimization goal) [YoHw95, 15]. At this point, we denote the dependency of the value vij of an attribute’s outcome aij as a value function () ij ij v f a=, or ( ) ij va (techniques for the attribute-wise rating of outcomes are presented in Subsection 3.2.2). We assume furthermore the following 36 We derive the value of the assigned weight wj from the frequency the j-th criterion is preferred. This method is all but unambiguous because the application of weight calculation formulas usually results in different, inconsistent values [YoHw95, 12–13]. We denote the criteria comparison matrix () {} {} × = = = ! ! \1, , , 1, , , mm im ij jm cCC with the cij as the relative importance of the j-th criterion towards the i-th one. Then inconsistency refers to preference statements which are intransitive and for which the consistency condition {} = ! i, j ,k 1, , ij ik kj ccc m with {}  = ! 1 i, j 1, , ij i j cww m does not hold [ZiGu91, 54–55], [YoHw95, 13]. For this reason we withdraw this approach and turn to the second one, a group of techniques called ratio weighting. These methods make use of ratios to display the trade-off between two attributes [Tria00, 57]. To be precise, we run again () 12mm×÷ pairwise comparisons of criteria, but in contrast to former techniques, we request ratio values from the DM which represent the preference ratio cij of one criterion over another, i.e. how many times is criterion i more important than criterion j [Tria00, 58–59]. As consistency implies reciprocity, we know that {}  =… 1 ,1,, ij ji cc i j m. We denote the weight vector () =!\ 1 Tm m www with {} > …0 1, , j w j m and define normalized weights, so that = =  1 1 m j j w. Then, weights are computed as follows [ZiGu91, 55–56]: {} = == =…   1 11 ,1,, m ij j jmm ij ij c wi j m c To assure consistency, the DM can either repeat the pairwise assessments and adjust the values or accept a certain error measure [EdNe90, 56–58]. ` Sophisticated techniques like Saaty’s eigenvalue approach or the modified least 37 square approach minimize this error value while determining optimal weights [BeSt02, 154–156], [Tria00, 57–60], [Saat80, 51]. When problems and criteria are complex, value trees facilitate defining criteria and assigning weights (Figure 17). Value trees make use of the hierarchical relation between criteria: Either an overall objective is decomposed top-down into several subordinate levels with families of criteria and child criteria, or inversely, criteria are composed to derive the paramount objective bottom-up. Then the DM compares each criterion with its siblings, and for each level comparison matrices are constructed and relative weights are derived [BeSt02, 140], [EdNe90, 62]. Convenient travel y Relative weight Cumulative weight Service 0,04 0,2 x Size 0,018 0,45 Upholstery 0,008 0,2 Foot space 0,014 0,35 Seat 0,12 0,6 Noise 0,04 0,2 Comfort 0,2 0,2 Cost 0,4 0,4 Duration 0,4 0,4 Top-down Bottom-up Convenient travel y Relative weight Cumulative weight Service 0,04 0,2 Service 0,04 0,2 0,04 0,2 x Size 0,018 0,45 Upholstery 0,008 0,2 Foot space 0,014 0,35 Size 0,018 0,45 Size 0,018 0,45 Size 0,018 0,45 0,018 0,45 Upholstery 0,008 0,2 Upholstery 0,008 0,2 Upholstery 0,008 0,2 0,008 0,2 Foot space 0,014 0,35 Foot space 0,014 0,35 Foot space 0,014 0,35 0,014 0,35 Seat 0,12 0,6 Noise 0,04 0,2 Seat 0,12 0,6 Seat 0,12 0,6 Seat 0,12 0,6 0,12 0,6 Noise 0,04 0,2 Noise 0,04 0,2 Noise 0,04 0,2 Comfort 0,2 0,2 Comfort 0,2 0,2 Comfort 0,2 0,2 0,2 0,2 Cost 0,4 0,4 Cost 0,4 0,4 Cost 0,4 0,4 Duration 0,4 0,4 Duration 0,4 0,4 Duration 0,4 0,4 Top-down Bottom-upTop-down Bottom-up Figure 17: Relative and cumulative weights in value trees (based on [BeSt02, 140]) The relevance of a criterion is eventually computed from the product of its relative weight and the relative weight of its parent and the parent’s parent and so forth. Reflecting the true relative importance to all given criteria, this value is called cumulative weight. We note that consistency has to be taken care of at every stage of assessment [BeSt02, 139], [Saat80, 78]. Regarding the sample scenario, we assume cardinal values for weights are given a priori and are subject to change as a measure taken by the trading entity. Furthermore, we will always elicit weights from the relative value of underlying preferences and implicitly include a consistency check (Figure 18). 38 Define weights Work out mweights w j Work out mweights w j Check consistency of weights Check consistency of weights [weights are consistent] [weights are inconsistent] Weights vector w m Weights vector w m Adjust weights vector Adjust weights vector Define weights Define weights Define weights Define weights Preference information Preference information Define weights Work out mweights w j Work out mweights w j Check consistency of weights Check consistency of weights [weights are consistent] [weights are inconsistent] Weights vector w m Weights vector w m Adjust weights vector Adjust weights vector Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Preference information Preference information Figure 18: The subprocess of defining weights 3.3 Multiple Attribute Decision Making 3.3.1 A Taxonomy of MADM Methods MADM methods are used when a finite (and countably small) number of alternatives with associated information on regarded criteria is given. The type of information provided by the DM influences the choice of method: Is preference information available or not and if so, what characterizes the salient feature of information (Figure 19) [ZiGu91, 29], [HwYo81, 8]? We start with a description of methods which do not need explicit preference information (Subsection 3.3.2) or merely ask for aspiration levels (Subsection 3.3.3), before we turn to approaches which require ordinal preference information (Subsection 3.3.4) or cardinal preference information (Subsection 3.3.5). 39 Type of information from DM Subsection MADM method/ class of methods Salient feature of information No information No information 3.3.2 Dominance Maximin Maximax Dominance Maximin Maximax 3.3.3 Conjunctive Method Disjunctive Method Conjunctive Method Disjunctive Method Standard level Standard level Attribute information Attribute information 3.3.4 Lexicographic Methods Elimination by Aspects Lexicographic Methods Elimination by Aspects Ordinal information Ordinal information 3.3.5 Simple Additive Weighting Weighted Product Method AHP TOPSIS Simple Additive Weighting Weighted Product Method AHP TOPSIS Cardinal information Cardinal information Type of information from DM Subsection MADM method/ class of methods Salient feature of information No information No information 3.3.23.3.2 Dominance Maximin Maximax Dominance Maximin Maximax 3.3.3 Conjunctive Method Disjunctive Method Conjunctive Method Disjunctive Method Standard level Standard level 3.3.33.3.3 Conjunctive Method Disjunctive Method Conjunctive Method Disjunctive Method Standard level Standard level Attribute information Attribute information 3.3.43.3.4 Lexicographic Methods Elimination by Aspects Lexicographic Methods Elimination by Aspects Ordinal information Ordinal information 3.3.5 Simple Additive Weighting Weighted Product Method AHP TOPSIS Simple Additive Weighting Weighted Product Method AHP TOPSIS Cardinal information Cardinal information 3.3.5 Simple Additive Weighting Weighted Product Method AHP TOPSIS Simple Additive Weighting Weighted Product Method AHP TOPSIS Cardinal information Cardinal information Figure 19: Overview of MADM methods (based on [HwYo81, 6]) 3.3.2 Deciding without Preference Information 3.3.2.1 Absence of Attribute Relevance When no information on the DM’s preference structure is given, a distinction between the relevance of all attributes is not possible. For all the methods following, advantages of one attribute cannot be traded for disadvantages of another; thus, trade-offs are not permitted. These methods are called non-compensatory, contrary to compensatory ones which allow offsetting superior with inferior values [YoHw95, 17]. 3.3.2.2 Dominance Principle The Dominance principle reduces the number of alternatives in a given set [Macc73, 31]. An alternative is nondominated if there is no other one in the set which excels it in at least one attribute while being equal in all other ones. All nondominated alternatives constitute the efficient frontier, the subset of Pareto efficient alternatives which should be taken into further consideration [KeRa93, 70]. In contrast, an alternative is called dominated when in comparison to another one it is defeated in at least one attribute while not excelling in another one. Dominated 40 alternatives play no role for further decision-making and can be eliminated from the set of alternatives [BeSt02, 83], [YoHw95, 18]. The graph below depicts a constellation with two attributes, where alternatives A and C are nondominated (they lie on the efficient frontier), and alternative B is defeated in both attributes by alternative C. The fictitious alternative D lies beyond the efficient frontier and is called unfeasible (Figure 20). Alternative D Alternative C Alternative A Attribute 1 Attribute 2 Alternative B Efficient frontier Efficient frontier Alternative D Alternative C Alternative A Attribute 1 Attribute 2 Alternative B Efficient frontier Efficient frontier Figure 20: Efficient frontier (based on [KeRa93, 71]) The Dominance principle can be used as a first-stage filter to isolate a subset of alternatives; with an increase in alternatives and attributes, it will less likely determine only one efficient option. 3.3.2.3 Maximin and Maximax When the decision-making context provides a tendency of preference, either in terms of a pessimistic or optimistic attitude towards the alternatives, we can make use of the Maximin or the Maximax method. Both methods do not require additional information about the DM’s preferences, but demand comparable attribute values, i.e. normalizing the attribute vectors in advance [ZiGu91, 43–44]. The Maximin method estimates the lowest value for each alternative and ranks all alternatives in descending order by their lowest value. The DM is advised to select the highest ranked alternative. This procedure is also called pessimistic, since only the 41 lowest value is taken into account and (possibly) superior values of other attributes cannot balance the one weakness [YoHw95, 28]. The Maximax method works rather similar; instead of the lowest, it identifies the highest value for each alternative which serves as a ranking criterion. Again, the DM is supposed to select the highest ranked option. This method is called optimistic, as it focuses merely on the highest value and disregards other inferior attributes [YoHw95, 30]. Table 9: Maximin and Maximax decision rules [YoHw95, 28–30] Method Selection rule Priority Precondition Maximin () {} *max min iij j i A Av= Lowest value (pessimistic attitude) Maximax () *max max iij ij A Av    =    Highest value (optimistic attitude) For nm× A\with {} 1,...,in=; {} 1,...,jm= and () [] {} 0;1 ij ij ij vvvav=  . Both procedures assign extreme weights of one hundred percent to one attribute (the lowest or highest) and of null percent to the remaining ones to determine the best alternative A* (Table 9) [ZiGu91, 44–45]. The two methods do not by all means lead to an advice for a single alternative, and they are due to their narrow focus disputable when it comes to withdrawing all but one criterion (the weakest one in the Maximin and the strongest one in the Maximax method) to justify the made decision [Macc73, 29]. Thus, we remove them from our future scope. 3.3.3 Satisficing (Conjunctive and Disjunctive Approaches) The idea of satisficing relates back to the work of Simon, who worked out the human inability of conducting rational behavior in decision-making. A DM rather concentrates on selecting an alternative which satisfies certain aspiration levels instead of seeking a global optimum [BeSt02, 104], [Simo66, 204–205]. The two types of heuristics based on satisficing are the Conjunctive and the Disjunctive approach. Whereas the former method is absolutely non-compensatory, the latter is diametrically opposite and perfectly compensatory. Instead of determining a single optimal solution, the two satisficing approaches divide the set of alternatives into two subsets of acceptable and unacceptable alternatives. While the latter are dis- 42 regarded from further consideration, the former comprise the number of relevant solutions [YoHw95, 20]. Satisficing requires aspiration levels which have to be set carefully because the thresholds determine the size of the resulting subsets: If the cutoff values are set high (low), the number of acceptable alternatives diminishes (soars), and if the DM fails to retrieve a feasible solution, he most likely will lower the aspiration levels [YoHw95, 20–21], [Simo55, 111]. When alternatives have to exceed the thresholds of all attributes to be considered as acceptable solutions, we use the Conjunctive approach. In this case an alternative is unacceptable, if at least one of the corresponding values fails to meet the minimum requirements [ZiGu91, 47]. The Disjunctive approach is less demanding than the Conjunctive one; the set of acceptable alternatives is defined by all alternatives which meet or exceed at least one threshold. Hence, the size of the subset of acceptable alternatives is much larger than the one in the Conjunctive approach [YoHw95, 21–22]. An overview of both heuristics and the formal relation to the given cutoff values aj0 is given below (Table 10). Table 10: Satisficing approaches [ZiGu91, 47–48] Method Acceptance rule Main implication Precondition Conjunctive  0 ij j aaj Non-compensatory Disjunctive {} 0 ij ij j aaa  Compensatory For nm× A\with {} 1, ,in=!; {} 1, ,jm=! and 0 j a\. Satisficing methods can be helpful to reduce the set of alternative and serve as a firststage filter for the DM [ZiGu91, 48]. The combination of both methods may also work well as a comprehensive filter for creating rules in repetitive decision-making [BeSt02, 105], [YoHw95, 22]. 3.3.4 Sequential Elimination 3.3.4.1 General Course of Action The idea of determining the optimal solution by sequentially eliminating alternatives names the next two MADM methods. If ordinally ranked attributes are given, the 43 Lexicographic Methods (LM) compare alternatives attribute-wise and withdraw dominated options until a single one remains. Similar, when no order for attributes is provided, Elimination by Aspects (EbA) removes all alternatives which do not satisfy attribute-wise standards until all but one are discarded. 3.3.4.2 Lexicographic Methods The name reflects the way this approach works: like words in a dictionary, alternatives are ranked step-wise (where words consist of letters, alternatives have attributes). In case specific attributes predominate others by importance, the DM can quickly estimate an optimal solution: Beginning with the most important attribute, we rank the alternatives and eliminate all but the best one. If more than a single alternative prevails, we repeat ranking and eliminating with the next most important attribute. The iteration stops when only one option remains [ZiGu91, 49–50]. Formal: Let n be the number of alternatives A, and m be the number of attributes to be maximized. Let k be the iteration step and {} {} 0 j AA=, {} 1, , j m!, we denote the rule {} {} 1max kk k j j AA x  = , which is repeated until {} 1 k A= or kn=, when all attributes have been used in the process and the final set of alternatives {} 1 n A is considered as equivalent [Webe93, 68]. A further explication of the formal background of LMs is given in [Fish74]. The improved Lexicographic Semiorder (LS) has its foundations in the work of Tversky and Luce [Tver69, 32], [Luce56, 181–182]. It uses the same procedure as the LM but requires significant differences between compared attributes before judging an alternative as dominating. In addition to the ranking of attributes, threshold levels are needed for attribute-wise comparisons [ZiGu91, 50–51]. LMs are intuitive, easily understandable, and do not require normalization of attribute ratings; their disadvantage is the neglect of lower ranked attributes, which cannot compensate for low values on higher ranked attributes [ZiGu91, 50], [Tver69, 46]. 44 3.3.4.3 Elimination by Aspects The EbA method has been initially proposed by Tversky and is similar to LMs, but the basic prerequisites differ in terms of information on attributes [Tver72, 285–287]: Instead of a ranking order, so-called standards for satisfaction have to be given. To attain the order for the aspect-wise elimination of alternatives, we investigate the ability of discrimination for each standard. This ability is determined by the number of alternatives eliminated by applying the standard of an aspect on the present set of alternatives. Thus, we begin eliminating with the aspect that discards the most alternatives and continue until one element remains [ZiGu91, 51–52]. Formal: Let n be the number of alternatives A, and m be the number of attributes to satisfy a specified standard. Let k be the iteration step with descending ability of discrimination so that {}{ } 1kk AA  , and with {} {} 0 j AA=, {} 1, , j m!, we denote the rule {} {} 1satisfies kk kj AA x  = , which is repeated until {} 1 k A= or kn=, when all attributes have been used in the process and the final set of alternatives {} 1 n A is again regarded as equivalent [YoHw95, 26]. The EbA approach combines ideas of the Conjunctive method and the LM: The practical application is lexicographically motivated and the elimination decision is based on the satisfaction of specified standards. But the relevance of attributes is completely ignored, and elimination happens rather arbitrarily than in a rational way [Webe93, 72], [ZiGu91, 52]. Tversky admits the inappropriateness of his method for many cases in the original work as well [Tver72, 298]. 3.3.5 Value Function Methods 3.3.5.1 Synthesizing Partial Values A well-known family of methods synthesizes partial value functions in order to determine a complete preorder of alternatives [Roy05, 15]. The calculation of an aggregate measure expects cardinal scaled information on the attribute outcomes as well as 45 weights for each attribute; how this vector of information is finally summarized into a scalar depends on the specific approach used [Tria00, 5]. This Subsection outlines the following four prominent methods: the Simple Additive Weighting (SAW), the Weighted Product Method (WPM), the Analytical Hierarchy Process (AHP), and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). 3.3.5.2 Simple Additive Weighting and Weighted Product Method The SAW approach, sometimes also referred to as the Weighted Sum Method, is particularly appealing due to its simple application [BeSt02, 87], [YoHw95, 32]. The step-by-step course of action is illustrated below (Figure 21). The SAW method assumes underlying additive value functions and computes an alternative’s score () ii VVA= by adding weighted normalized values {} = ! 1, , jij wv j m before eventually ranking alternatives on this aggregate (Table 11, p. 47). Two additional preconditions are fundamental for this technique, the preferential independence of partial values and the assessment of weights in proportion to the relative value of the criterion [YoHw95, 33], [Wins94, 773–774]. As we only determine weights from aggregating conversion ratios, the second precondition is of less importance here. Apart from that, preferential independence relates to the absence of interdependencies between the partial value functions: This means the contribution of an individual attribute value to the aggregate is not affected by any other attribute [Dyer05, 274– 275], [KeRa93, 129]. Proof of this necessary condition is given in [Fish76, 248]. 52 The name of the approach does not fully reflect the process: It determines the preference order on the grounds of the similarity to a positive ideal solution and the dissimilarity to a negative solution. Computing the distance of each considered alternative to those ideal solutions makes use of the Euclidean distance vector; for the twoattribute case this is depicted below using a two-dimensional coordinate system (Figure 26) [HwYo81, 128]. Though alternative one is closer to the positive ideal solution than alternative two, the approach may still favor the latter due to the greater distance to the negative ideal solution compared to alternative one. Attribute 2 (increasing preference) Attribute 1 (increasing preference) Alternative 2 Alternative 1 A + (positive ideal solution) A - (negative ideal solution) Attribute 2 (increasing preference) Attribute 1 (increasing preference) Alternative 2 Alternative 1Alternative 1 A + (positive ideal solution) A - (negative ideal solution) Figure 26: Euclidean distances to the ideal solutions in two-dimensional space [HwYo81, 129] Therefore, if we want to rank alternatives with respect to two reference points, we have to construct these boundaries in advance. The step-by-step procedure is outlined below (Figure 27). First, starting with a given decision matrix, we need to get comparable values vij in each matrix entry. This is achieved with a modified vector normalization and multiplication with the corresponding weights wj [FeWa01, 465], [HwYo81, 131]. 53 Technique for Order Preference by Similarity to Ideal Solution Define decision matrix Define decision matrix Decision matrix Decision matrix Sort alternatives by similarity Ri Sort alternatives by similarity Ri Define weights Define weights Define weights Define weights Derive partial values v with vector normalization Derive partial values v with vector normalization Weights vector wm Weights vector wm Decision matrix with values Vnxm Decision matrix with values Vnxm Positive ideal solution A+ Positive ideal solution A+ Negative ideal solution ANegative ideal solution ADetermine separation measures S+ Determine separation measures S+ Determine separation measures SDetermine separation measures SConstruct positive ideal solution A+ Construct positive ideal solution A+ Construct negative ideal solution AConstruct negative ideal solution ACompute weighted values wj ×v ij Compute weighted values wj ×v ij Calculate similarity to ideal solution Calculate similarity to ideal solution Similarity R for all alternatives Similarity R for all alternatives Ranking Ranking Data Data Technique for Order Preference by Similarity to Ideal Solution Define decision matrix Define decision matrix Define decision matrix Define decision matrix Decision matrix Decision matrix Sort alternatives by similarity Ri Sort alternatives by similarity Ri Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Derive partial values v with vector normalization Derive partial values v with vector normalization Weights vector wm Weights vector wm Decision matrix with values Vnxm Decision matrix with values Vnxm Positive ideal solution A+ Positive ideal solution A+ Negative ideal solution ANegative ideal solution APositive ideal solution A+ Positive ideal solution A+ Negative ideal solution ANegative ideal solution ADetermine separation measures S+ Determine separation measures S+ Determine separation measures SDetermine separation measures SDetermine separation measures S+ Determine separation measures S+ Determine separation measures SDetermine separation measures SConstruct positive ideal solution A+ Construct positive ideal solution A+ Construct negative ideal solution AConstruct negative ideal solution AConstruct positive ideal solution A+ Construct positive ideal solution A+ Construct negative ideal solution AConstruct negative ideal solution ACompute weighted values wj ×v ij Compute weighted values wj ×v ij Calculate similarity to ideal solution Calculate similarity to ideal solution Similarity R for all alternatives Similarity R for all alternatives Ranking Ranking Data Data Figure 27: Process of the Technique for Order Preference by Similarity to Ideal Solution In the second step, we construct two virtual ideal alternatives, A+ consisting of all best criteria values vj+ (the positive ideal solution), and the negative ideal solution Awith all the poorest values vj- (Table 12) [HwYo81, 131]. Table 12: Assembling positive and negative ideal solutions [HwYo81, 131] Values Precondition Positive ideal solution {} {} :max jijj i Av vw ++ = Negative ideal solution {} {} :min jijj i Av vw  = For × \nm Vwith {} =…1, ,in; {} =! 1, , j m and [ ] ,0;1 ij j vw 54 These two vectors represent extreme points in a Cartesian coordinate system, and all given alternatives are located between them, i.e. all alternatives can be constructed from linear combinations of these points (Figure 26). The method makes use of this particular feature: in the third step, we compute separation measures S+i (S-i) as indicators for the distance of each alternative from the positive (negative) reference point [HwYo81, 132]. () {} ++ = == ! 2 1 1, , m ijijjj j Swvwvin () {}  = == ! 2 1 1, , m ijijjj j Swvwvin We do not rely merely on the closeness to the positive ideal solution but rather on both distances, since the shortest positive difference does not necessarily mean it is also least close to the negative ideal one; the distance vectors depicted above (Figure 26) illustrate a case in which one alternative (number one) is closer to the positive ideal and to the negative ideal solution then another one (number two). The fourth step is concerned with computing the similarity to ideal solution measure and ranking the alternatives. Given the two distance indices for each alternative, we calculate the similarity measure Ri as follows [HwYo81, 132]: {} 1, , i i ii S Rim SS  + == +! with [] 0;1 i R The closer the similarity measure Ri is to one, the more preferable is the alternative; with a decreasing (increasing) difference to the negative (positive) ideal solution, the alternative becomes the less interesting [HwYo81, 132]. Fifth and finally, we can sort our alternatives in ascending order by the similarity measure and recommend the top-ranked option [HwYo81, 132]. Advising DMs with the help of a TOPSIS evaluation seems very appealing and applicable in concrete situations; reason is the similarity to the SAW method [HwYo81, 135–136]. Meanwhile, the method has been extended to situations with continuous solution sets, which usually require extensive linear programming [HLLi93, 890]. But a problem arises when cardinal values are not given or when the underlying utility is not subject to monotonicity [HwYo81, 137]. As we already ruled out the latter in our definitions (cf. Subsection 2.6.4), one may feel tempted to solve the former by 55 transforming ordinal or nominal information. Unfortunately, this may lead to distortion (e.g. when intervals between values are not constant); in this case the technique may become a merely superficial recommendation (cf. also Subsection 3.2.1). On top of that, Wang and Triantaphyllou claim to have found evidence that the TOPSIS method also suffers from ranking irregularities (cf. AHP, Subsection 3.3.5.3) [WaTr08, 46]. 3.4 Multiple Objective Decision Making 3.4.1 Overview of MODM Methods In contrast to MADM methods, the set of alternatives in Multiple Objective Decision Making is not pre-defined: To cope with an infinite or continuous space of options, specified constraints and objective functions define the domain from which an optimal solution is to be “designed”. [ZiGu91, 25], [HwMa79, 6–7]. Such decision problems, in which multiple objectives are to be optimized, have been initially referred to as vector maximum problems [KuTu51, 488]. In MODM, the DM’s preference information is implemented in terms of aspiration or satisfaction levels for criteria. These levels may either be minimum (maximum) prerequisites when the corresponding objective is to be maximized (minimized), or an exact value which should be hit as close as possible [BeSt02, 210]. Hwang and Masud classify MODM methods on the type of information needed (Figure 28). A full introduction into the foundations of MODM and the classified methods can be found in their monograph [HwMa79]. Of these classes of methods, we will sketch the idea of Goal Programming in the following Subsection. 56 Stage at which information is needed Major classes of methodsType of information • Global Criterion Method • Global Criterion Method • Lexicographic Method •Goal Programming Method • Goal Attainment Method • Lexicographic Method •Goal Programming Method • Goal Attainment Method • Method of Geoffrion and Interactive Goal Programming • Surrogate Worth Trade-off Method • Method of Satisfactory Goals • Method of Zionts-Wallenius • Method of Geoffrion and Interactive Goal Programming • Surrogate Worth Trade-off Method • Method of Satisfactory Goals • Method of Zionts-Wallenius • Parametric Method ವˢ-constraint Method • MOLP Methods • Adaptive Search Method • Parametric Method ವˢ-constraint Method • MOLP Methods • Adaptive Search Method No articulation of preference information No articulation of preference information Progressive articulation of preference information (Interactive methods) Progressive articulation of preference information (Interactive methods) A priori articulation of preference information A priori articulation of preference information A posteriori articulation of preference information (Nondominated solutions generation method) A posteriori articulation of preference information (Nondominated solutions generation method) • Utility Method • Bounded Objective Method • Utility Method • Bounded Objective Method Explicit trade-off Explicit trade-off Implicit trade-off Implicit trade-off Implicit trade-off Implicit trade-off Cardinal information Cardinal information Ordinal and cardinal information Ordinal and cardinal information • STEM and related methods • SEMOPS and SIGMOP methods • Method of Displaced Ideal • GPSTEM method • Method of Steuer (Interactive MOLP method) • STEM and related methods • SEMOPS and SIGMOP methods • Method of Displaced Ideal • GPSTEM method • Method of Steuer (Interactive MOLP method) Stage at which information is needed Stage at which information is needed Major classes of methodsMajor classes of methodsType of informationType of information • Global Criterion Method • Global Criterion Method • Lexicographic Method •Goal Programming Method • Goal Attainment Method • Lexicographic Method •Goal Programming Method • Goal Attainment Method • Method of Geoffrion and Interactive Goal Programming • Surrogate Worth Trade-off Method • Method of Satisfactory Goals • Method of Zionts-Wallenius • Method of Geoffrion and Interactive Goal Programming • Surrogate Worth Trade-off Method • Method of Satisfactory Goals • Method of Zionts-Wallenius • Parametric Method ವˢ-constraint Method • MOLP Methods • Adaptive Search Method • Parametric Method ವˢ-constraint Method • MOLP Methods • Adaptive Search Method No articulation of preference information No articulation of preference information Progressive articulation of preference information (Interactive methods) Progressive articulation of preference information (Interactive methods) A priori articulation of preference information A priori articulation of preference information A posteriori articulation of preference information (Nondominated solutions generation method) A posteriori articulation of preference information (Nondominated solutions generation method) • Utility Method • Bounded Objective Method • Utility Method • Bounded Objective Method Explicit trade-off Explicit trade-off Implicit trade-off Implicit trade-off Implicit trade-off Implicit trade-off Cardinal information Cardinal information Ordinal and cardinal information Ordinal and cardinal information Explicit trade-off Explicit trade-off Implicit trade-off Implicit trade-off Implicit trade-off Implicit trade-off Cardinal information Cardinal information Ordinal and cardinal information Ordinal and cardinal information • STEM and related methods • SEMOPS and SIGMOP methods • Method of Displaced Ideal • GPSTEM method • Method of Steuer (Interactive MOLP method) • STEM and related methods • SEMOPS and SIGMOP methods • Method of Displaced Ideal • GPSTEM method • Method of Steuer (Interactive MOLP method) Figure 28: A taxonomy of methods for Multiple Objective Decision Making [HwMa79, 8] 3.4.2 Goal Programming The first Goal Programming (GP) practice can be traced back to Charnes et al. who estimated a fair compensation for company executives [CCFe55]. Later, Charnes and Cooper developed the basic concept of GP as means for “goals, even when they are unattainable within the limits of available resources” [ChCo67, 215]. The GP technique has since then received wide acceptance in various fields, e.g. 265 reference cases can be found in [JoTa02, 134–136] and a bibliography of 443 classed entries is provided by [Rome91, 100–105]. 57 The basis of GP is a linear programming problem with the following constraints presented in [ChCo67, 216]: 12 1 12 12 12 32 12 510 8 4 ,0 xx x xx xx xx +  + +   Depicting the problem with its constraints reveals two (orange and blue) shaded areas with partly feasible solutions, but since both subsets do not overlap, no set of feasible solutions exists which satisfies all constraints (Figure 29) [ChCo67, 217]. x1 x2 10 5 0510 5x 1 10 -x 1 + x 2 4 x 1 + x 2 8 3x 1 + 2x 2 12 x1 x2 10 5 0510 5x 1 10 -x 1 + x 2 4 x 1 + x 2 8 3x 1 + 2x 2 12 Figure 29: Portray of feasible solutions in a GP example [ChCo67, 216] Now, the GP idea is to introduce two deviation variables di- (for underachievement) and di+ (for overachievement) when measuring the attainment of a target ti by an objective i [Lee99, 8-2–8-3]. Then we seek to minimize an achievement function z that consists of the weighted deviations of all q objectives. We can denote the linear GP problem as () () 1 min subject to ,,, 0 0 q ii ii i iii i iiii ii znwdpwd fx d d t nw pw d d nw pw + = + + =+ + =  =  {} 1, ,i q = !, 58 under the assumption all objectives are normalized [JoTa02, 130–131]. Since we model relative importance between objectives by applying weights (nwi, pwi), this particular type of GP problem is called weighted GP or Archimedean GP [JoTa02, 130], [ZiGu91, 122]. The modified simplex method solves this problem [Lee72, 105–106]. In the wide array of GP extensions, two other major variants stand out notably often: Lexicographic (or preemptive) GP and Chebyshev (or minmax) GP [Lee99, 8-4–86], [Igni85, 12–13]. Preemptive GP strives to attain objectives in a predefined priority order and is helpful when the DM cannot quantify the relative importance of goals. As the approach does not allow trade-offs between priority levels, the DM should have a natural order of objectives in mind [JoTa02, 132]. Preemptive GP is solved by a sequence of linear programs; a formal outline is given in [Lee99, 8-5–8-6]. Chebyshev GP aims at a shortcoming of Archimedean GP: if a large number of deviations are very small, few very large deviations do not preponderate in the attainment function. In order to ameliorate this inconvenience, the Chebyshev GP approach minimizes the maximum weighted deviation [JoTa02, 132–133], [ZiGu91, 124]. () min subject to ,,, 0 0 ii ii iii i iiii ii zMax nw d p wd Max fx d d t nw pw d d nw pw + + + = + + =  = {} 1, ,i q = ! In result, the heuristic balances the levels of objectives instead of sticking to a strict minimisation of their sum. This reflects the attitude of a careful DM, similar to the Maximin approach in MADM (Table 9). Currently, research on the issue of GP includes non-linear GP, fractional GP, integer GP and interactive GP. The integration and combination with other techniques such as the AHP or the Data Envelopment Analysis (DEA) plays also an important role [JoTa02], [Lee99]. In terms of the DEA, which determines an efficient frontier from a domain of alternatives, defining upper and lower bounds for weights and conducting sensitivity analysis are of interest (for an explication of the DEA method see the original work of [CCRh78] ) [BeSt02, 303], [JKWa98], [Stew96]. 59 GP operationalizes Simon’s concept of satisficing insofar as functions for objectives are given and the DM specifies his aspiration levels (goals) (cf. p. 41). Though the technique is widely regarded as an “intuitive and comfortable approach“, it is not flawless [BeSt02, 231]: setting realistic goals in advance can constitute a major pitfall and may lead either to “no alternative, or very large numbers of alternatives, which satisfy the goals” [Stew92, 576]. Especially when complex or unfamiliar problems are concerned, the DM will hardly be aware of specific target levels. Thus the use of GP is recommended for screening purposes i.e. for producing a subset of feasible alternatives [EhWi05], [Stew92, 578]. 3.5 Decision Aids 3.5.1 Outranking Relations The methods in this Section differ from the previous ones insofar, as they explicitly permit incomparable alternatives and criteria, and do not require transitivity or completeness in the arrangement of alternatives [BeSt02, 104–105], [Roy73, 181–183]. The intent of outranking is not so much retrieving an optimal solution but rather reducing the number of given alternatives to a non-dominated set from which the DM is supposed to select afterwards; for this reason these methods are called aids [ZiGu91, 202]. The relation between two alternatives A1 and A2 is assessed with the help of a binary outranking relation S, in comparing pairs of alternatives, which leads to three possible relations (Table 13) [Roy73, 181–182]. Table 13: Outranking relations [Roy73, 181–182] Strict preference1 Indifference Incomparability A1SA2 and not A2SA1 A1SA2 and A2SA1 Not A1SA2 and not A2SA1 12 AA; 12 AA 12 AA/ A1 is strictly preferred to A2 A1 is indifferent to A2 A1 is incomparable to A2 1) applies to the inverse relation as well The inclusion of incomparable relations is useful for modeling a preference order when the DM is incapable or unwilling to distinguish [Roy73, 182–183]. We outline the oldest family of methods, called ELECTRE, in the following Subsection [ZiGu91, 207]. 60 Apart from ELECTRE, another class of methods named PROMETHEE (acronym for Preference Ranking Organization METhod for Enrichment Evaluations) is widespread in outranking research [BeSt02, 233]. For an introduction with latest developments we refer to [BrMa05] or the original publication [BVMa86]. 3.5.2 The ELECTRE Approach The family of ELECTRE methods was initially developed in 1965, and the first ELECTRE method was officially published three years later [Roy68]. The acronym ELECTRE is deduced from ELimination Et Choix Traduisant la REalité (ELimination and Choice Expressing the REality) [Tria00, 13], [Roy68]. For a summary of six ELECTRE methods, namely ELECTRE I, II, III, IV, IS, and TRI, we refer to [Vinc99, 11-5–11-10]. The oldest and simplest of these, ELECTRE I, is presented in this Subsection. ELECTRE methods have been applied to a wide field of concrete decision problems, including environmental planning ([GSM+03], [SHLa98], [TeTz94]), employee recruitment ([SGKM07]), location planning ([Nore06], [BDLe90]), transportation management ([RoHu82]) and financial issues ([MKBe88]). The underlying principle of ELECTRE is the following: We compare alternatives pairwise and assess the extent to which an alternative is outranking another and up to which extent this is not the case. In order to outrank an alternative, sufficient evidence for the assumption (concordance) and insufficient evidence against the assumption (discordance) are needed. The strength of an evidence is determined by the evaluation of constructed concordance and discordance measures for each comparison [ZiGu91, 207]. The course of action is illustrated below (Figure 30) and the five steps of the ELECTRE I method are described in the next paragraphs. First, we need a normalized and weighted decision matrix, although incomparability is allowed; for ELECTRE methods, it is common practice to apply the vector normalization [Tria00, 13]. 61 ELECTRE Define decision matrix Define decision matrix Decision matrix Decision matrix Define weights Define weights Define weights Define weights Derive partial values v with vector normalization Derive partial values v with vector normalization Weights vector wm Weights vector wm Decision matrix with values Vnxm Decision matrix with values Vnxm Compute weighted values wj × vij Compute weighted values wj × vij Data Data <<localPrecondition>> Couples of alternatives left, which are not compared yet <<localPrecondition>> All alternatives compared Determine set of concordance indices Determine set of concordance indices Determine set of discordance indices Determine set of discordance indices Compare alternatives pairwise on each criterion Compare alternatives pairwise on each criterion Quantify strength of concordance indices conkl Quantify strength of concordance indices conkl Quantify strength of discordance indices disckl Quantify strength of discordance indices disckl Select pair of alternatives Select pair of alternatives B Calculate mean strength of discordance Calculate mean strength of discordance Discordance threshold value Discordance threshold value Build discordance dominance matrix G Build discordance dominance matrix G Discordance dominance matrix G Discordance dominance matrix G Concordance dominance matrix F Concordance dominance matrix F Calculate mean strength of concordance Calculate mean strength of concordance Concordance threshold value Concordance threshold value Build concordance dominance matrix F Build concordance dominance matrix F Kernel of leading alternatives Kernel of leading alternatives Eliminate dominated alternatives Eliminate dominated alternatives Compute dominance matrix E Compute dominance matrix E Dominance matrix E Dominance matrix E B A A A ELECTRE Define decision matrix Define decision matrix Define decision matrix Define decision matrix Decision matrix Decision matrix Define weights Define weights Define weights Define weights Derive partial values v with vector normalization Derive partial values v with vector normalization Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Define weights Derive partial values v with vector normalization Derive partial values v with vector normalization Weights vector wm Weights vector wm Decision matrix with values Vnxm Decision matrix with values Vnxm Weights vector wm Weights vector wm Decision matrix with values Vnxm Decision matrix with values Vnxm Compute weighted values wj × vij Compute weighted values wj × vij Data Data <<localPrecondition>> Couples of alternatives left, which are not compared yet <<localPrecondition>> Couples of alternatives left, which are not compared yet <<localPrecondition>> Couples of alternatives left, which are not compared yet <<localPrecondition>> All alternatives compared <<localPrecondition>> All alternatives compared <<localPrecondition>> All alternatives compared Determine set of concordance indices Determine set of concordance indices Determine set of discordance indices Determine set of discordance indices Determine set of concordance indices Determine set of concordance indices Determine set of discordance indices Determine set of discordance indices Compare alternatives pairwise on each criterion Compare alternatives pairwise on each criterion Quantify strength of concordance indices conkl Quantify strength of concordance indices conkl Quantify strength of discordance indices disckl Quantify strength of discordance indices disckl Quantify strength of concordance indices conkl Quantify strength of concordance indices conkl Quantify strength of discordance indices disckl Quantify strength of discordance indices disckl Select pair of alternatives Select pair of alternatives B Calculate mean strength of discordance Calculate mean strength of discordance Discordance threshold value Discordance threshold value Build discordance dominance matrix G Build discordance dominance matrix G Discordance dominance matrix G Discordance dominance matrix G Concordance dominance matrix F Concordance dominance matrix F Calculate mean strength of concordance Calculate mean strength of concordance Concordance threshold value Concordance threshold value Build concordance dominance matrix F Build concordance dominance matrix F Kernel of leading alternatives Kernel of leading alternatives Eliminate dominated alternatives Eliminate dominated alternatives Compute dominance matrix E Compute dominance matrix E Dominance matrix E Dominance matrix E B A A A Figure 30: Process of the ELECTRE method Secondly, the strength of concordance and discordance are determined for each couple of alternatives. The comparison of two alternatives is conducted using the outranking relation S on each j-th criterion separately, thus it is not as strict as the formal rules of the value function methods. 68 Referring to the Section 2, we now turn to the object-related prerequisites, assuming the agent is buying a commodity. This means except for the price, offers cannot be differentiated (service measures like terms of delivery are omitted). But beyond product characteristics, the agent considers image and social reputation of a seller. Thus, three criteria are subject of the decision problem. More important, on a super large-scaled marketplace, it is very likely that no image but only a social reputation value is available, thus we need a compensatory method which allows trade-offs between criteria (cf. 2.5.2.1). To allow compensation, we assume the relations between the three criteria are independent in our simplified case. If that holds for price and reputation in everyday life is questionable – and to be strict, in the sense of ReGreT, image exerts a slight influence on social reputation. Due to the tremendous number of market participants, we assume this effect to be insignificantly small. Otherwise all methods based on additive utility assumptions would have to be disregarded. Weights Weights Aspiration levels Aspiration levels Result Result Preference information Preference information Criteria Criteria Independence Independence Compensatory Compensatory Input Input Output Output Input compliance Input compliance V = = Output compliance Output compliance   One distinct solution One distinct solution Set of efficient solutions Set of efficient solutions  Weights Weights Aspiration levels Aspiration levels Weights Weights Aspiration levels Aspiration levels Result Result Preference information Preference information Criteria Criteria Independence Independence Compensatory Compensatory Input Input Output Output Input compliance Input compliance VV == == Output compliance Output compliance   One distinct solution One distinct solution Set of efficient solutions Set of efficient solutions  One distinct solution One distinct solution Set of efficient solutions Set of efficient solutions  Figure 33: Prerequisites for the appropriate MCDM method Second, we address the output side of the MCDM method: The result of the decision-making process has to be a specific recommendation in terms of one offer to bid for, i.e. non-interactivity from the DM’s point of view is essential. MCDM approaches which merely generate a set of efficient solutions are of little help, since they require interaction with the principal to continue bidding. Those interactions are to be avoided, as they delay the fulfillment process and thus impede the system efficiency (for the facets of interactivity in terms of interactive MCDM approaches see [Stew99, 10-2–10-3]). 69 Now as we have compiled all the prerequisites, we need to confront them with the features of the discussed methods. To facilitate the comparison, we listed all techniques below (Table 16, 69). The dimensions of information given in the overview are explained in the table before (Table 15). Table 15: Dimensions of the comparison table Method Name or acronym of the method as given in this work Type MADM MADM method MODM MODM method Outranking Outranking method (Decision aid) Set of options Size of the set of alternatives Finite Bounded to a countable number Infinite Unrestrained and not-countable large Scale level (Scale level required) Minimum level at which given informations have to be scaled Norm (Normalization ) Yes/ No Normalized information required Comp (Compensatory) Yes/ No Rather compensatory Pref (Preference modeling) Yes/ No Known preferences of the DM modeled in the method Output (Output of the MCDM method) 0 Rather a single solution; non-interactive 1 Single solution or set of efficient alternatives equally possible 2 Rather a set of efficient alternatives Supplementary information In addition to the decision matrix needed information Set of supplementary information Extent to which supplementary information is needed Case Yes/ No Computed example provided in case study in Appendix B Ref (Reference) Points to the Subsection of the method 70 Table 16: Comparison of MCDM methods Ref 3.3.2.2 3.3.2.3 3.3.3 3.3.3 3.3.4.2 3.3.4.3 3.3.5.2 3.3.5.2 3.3.5.3 3.3.5.4 3.4.2 3.5.2 Case Yes Yes Yes No Yes Yes Yes Yes Yes Yes No Yes Set of supplementary information - - m m m m m m at least [m × (m-1) + m × n ×(n-1)] ÷2 (three-level hierarchy)a m m m Supplementary information - - Aspiration levels Aspiration levels Attribute order of relevance Standards Weights for attributes; values derived from outcomes Weights for attributes; outcomes  1 Relative importance of criteria and alternatives with respect to parental nodes Weights for attributes Weights for attributes; aspiration levels Weights for attributes Output 2 0 2 2 1 1 0 0 0 0 1 2 Pref No No Yes Yes Yes No Yes Yes Yes Yes Yes Yes Comp No No No Yes No No Yes Yes Yes Yes Yes No Norm No Yes No No No No Yes No Yes Yesb Yes Yesb Scale level Ordinal Ordinal Ordinal Ordinal Nominal Ordinal Cardinal Cardinal Cardinal Cardinal Cardinal Ordinal Set of options Finite Finite Finite Finite Finite Finite Finite Finite Finite Finite Infinite Finite May also be derived from (m × n) given values Vector normalization by developers recommended Type MADM MADM MADM MADM MADM MADM MADM MADM MADM MADM MODM Outranking a b Method Dominance Maximin/ Maximax Satisficing (Conjunctive) Satisficing (Disjunctive) Lexicographic Methods EbA SAW WPM AHP TOPSIS Goal Programming ELECTRE (I) 71 4.2.3 Conclusion for Method Application With the help of the comparison table and the input and output prerequisites, we can depict the discussed methods on a two-axis chart. The method for our scenario should be one of the equally suitable four in the upper right quarter (Figure 34). Preferred methods Preferred methods 11 10 9 8 1 6 2 5 3 12 4 Output compliance Legend (1) Dominance (2) Maximin/ Maximax (3) Conjunctive Approach (4) Disjunctive Approach (5) Lexicographic Methods (6) EbA (7) SAW (8) WPM (9) AHP (10) TOPSIS (11) Goal Programming (12) ELECTRE Input compliance 7 Preferred methods Preferred methods 1111 1010 99 88 11 66 22 55 33 1212 44 Output compliance Legend (1) Dominance (2) Maximin/ Maximax (3) Conjunctive Approach (4) Disjunctive Approach (5) Lexicographic Methods (6) EbA (7) SAW (8) WPM (9) AHP (10) TOPSIS (11) Goal Programming (12) ELECTRE Input compliance 77 Figure 34: Classification of MCDM methods in the light of the scenario At this stage, we bestow consideration upon the complexity of each method in a nutshell: The SAW method and WPM are probably the most straightforward methods and constitute no insurmountable obstacle in determining aggregates from m×n outcomes. The TOPSIS comprises eliciting minimum and maximum values for all m criteria from the given set of n alternatives, as well as calculating n distance vectors. These m×n computations are manageable as well, even for a huge set of alternatives. A sharp contrast is the AHP – with an increasing number of n alternatives for m criteria, the number of pairwise comparison matrices, which have to be processed, with each matrix subject to ( ) 12nn  ÷  evaluations, soars by the factor of m, means incrementally about m×n² evaluations (e.g. 100 alternatives and three criteria already need 14.853 comparisons, cf. p. 51) [Brug04, 310]. Hence, we eliminate the AHP from our list. Concerning the remaining three approaches, we choose the TOPSIS method for one reason: If we store the current ideal solution vectors in a repository database, we are 72 able to trace the experiences our agent has made and the development he underwent. We will explicate this in more detail in Subsection 4.4.1. Apart from our decision, two other practices are to be considered when solving a multiple criteria decision problem: On the one hand, we could build a system of rules, which filters insufficient alternatives stepwise, e.g. by combining Conjunctive and Disjunctive approaches. Such a system would be equivalent to the way in which we decided above on the MCDM method. That means, we would equip the agent with a set of rules consisting of ranges or bounds for criteria values for which we consider an alternative to be satisfying [Ozer88, 246–247]. Even though the agent would not seek the best, but merely satisfying solution, this procedure may be preferable when extensive computations jeopardize the system’s stability or when processing power becomes a bottleneck; we assume this does not apply to the case of our future scenario. On the other hand, we could employ simultaneously different MCDM methods, let each one determine the optimal solution, aggregate the ranked sets and synthesize them afterwards [HwYo81, 214]. But especially when dealing with a large number of criteria or alternatives, this may seriously threaten a system’s overall performance. We take note of both ideas here, but do not contemplate the implementation for the above stated reasons. 4.3 Scenario Specifications 4.3.1 Environment and Actors Our ALN consists of a very large number of individual computer systems, each one offering limited storage capacity for hire on payment of a fee. Every computer system belongs to a principal and is represented by an agent, which at a particular time is either offering or seeking storage capacity. A central institution collects offers from sellers, enriches them with reputation information and forwards them to buyers. Because this intermediary also provides access to the network, we call it the hub (Figure 35). 73 ALN ALN Agent Agent (Human) Principal (Human) Principal Hub Hub Computer system Computer system is owner of ALN ALN Agent Agent (Human) Principal (Human) Principal Hub Hub Computer system Computer system is owner of Figure 35: Scheme of the scenario 4.3.2 Interaction between Actors On the basis of the already illustrated main process in Section 2 (Figure 32, p. 66), we explain in detail the interaction of buyer, seller and hub within the ALN in the following paragraphs (for a UML sequence diagram see Figure 36): Whenever an agent receives a demand note for hard disk space from his connected system, he sends out a request for offers to the hub. The hub collects current offers from his offer database and searches his reputation databases for impression entries corresponding with the current sellers; if entries are available, reputation is calculated and attached to the offer information. Then the hub forwards the information package to the requesting agent. After the buyer receives the current available offers from the hub, he browses his own image database for previous experiences with the present sellers and if available, adds the image value to the corresponding offer. With this information, the MCDM procedure is carried out, a best alternative is determined and the buyer submits his price quote to the seller. When negotiations are successfully finished, the transaction is fulfilled by transferring payment and accessing the hard disk partition for storing data (this step is subsumed under the term delivery). 74 create_entry(impression) get_offers() return_array (seller, offer) store(seller, offer) Ok=store() Buyer Buyer Buyer‘s image database Buyer‘s image database Hub Hub Offer database of hub Offer database of hub Reputation database of hub Reputation database of hub Seller Seller par loop loop alt break provide_offer(price, quantity) request_offer() MCDM return_array(seller, offer, rep) submit_quote(bid) reject() accept() payment(bid) delivery() feedback(impression) create_entry(impression) Ok=create_entry() get_seller_reputation() return_seller_reputation(rep) return_void() alt Ok=create_entry() Ok=feedback() sd get_seller_image() return_seller_image(img) return_void() alt create_entry(impression) get_offers() return_array (seller, offer) store(seller, offer) Ok=store() Buyer Buyer Buyer‘s image database Buyer‘s image database Hub Hub Offer database of hub Offer database of hub Reputation database of hub Reputation database of hub Seller Seller parpar looploop looploop altalt breakbreak provide_offer(price, quantity) request_offer() MCDM return_array(seller, offer, rep) submit_quote(bid) reject() accept() payment(bid) delivery() feedback(impression) create_entry(impression) Ok=create_entry() get_seller_reputation() return_seller_reputation(rep) return_void() altalt Ok=create_entry() Ok=feedback() sdsd get_seller_image() return_seller_image(img) return_void() altalt Figure 36: Interaction within the ALN 75 Afterwards, the buyer sends feedback in terms of an impression tuple to the hub, which stores this information in the associated reputation databases. The buyer simultaneously adds impressions to his image database for future consultation. While prospective buyers communicate with the hub, the offer database is fed continuously by selling agents, as long as capacity is for sale. 4.3.3 Offer Attributes The three distinguishing attributes associated with an offer are price, social reputation and image (Table 17). The buying agent strives to maximize all of these attributes, except for the price. Table 17: Offer attributes Attribute Symbol Goal Source Domain Special case Price of offer i PRi Minimize Seller (through hub) [[ 0; i PR Social reputation of seller of offer i SRi Maximize Hub’s SDB and IDB [] 0;1 i SR [] /   =0;1 0.5 ii SR SR Image of seller of offer i IMi Maximize Buyer’s ODB [] 0;1 i IM [] /   =0;1 0.5 ii SR SR The price is initially set by the seller and varies with the number of offers and request from agents due to the nature of the price mechanism, the English auction: a surging demand leads to rising prices, a dropping one cuts prices (cf. Subsection 2.4.2.3, p. 15). The posted price relates always to a specified amount of capacity (one GB) and period for which the capacity is provided (e.g. one month). This unit of “price per GB per month” is assumed to be mutually accepted and fixed – no variances are possible and if capacity is needed for less than a month or less than a GB is required, the price will still have to be paid for the full unit and the complete term. We assume that a price is always positive and that there is no upper bound. Social reputation is no mandatory information: in case no feedback on the seller has been provided yet, no reputation value exists. The sources for reputation information are the SDB and the IDB, and both databases are locally maintained by their parent hub (cf. Subsection 2.5.2.3, p. 22). The hub automatically accesses his databases, re- 76 trieves available information and calculates social reputation. The resulting value is normalized on an interval from zero to one with a value of one indicating the best judgment of one’s reputation, whereas values close to zero represent very bad reputation. Image is similar to social reputation in almost all terms except for its origin. The source of image is the buyer’s ODB with impression entries from previous encounters with sellers (cf. Subsection 2.5.2.3, p. 21). Although the buyer controls the computation of image values, we do not examine different levers for manipulating this process. Image is also provided on a scale from zero to one, with the value of one being a sign for exceptionally positive previous encounters, and the value of zero meaning the seller is least trustworthy. Since an agent has access to exactly one hub, he can neither monitor a current overall marketprice nor compute a market equilibrium [Vari06, 572]. The only key figure one may compute are local mean or deviation measures of the given offers, but these figures are not needed here. If an image or social reputation value is not provided, we put the scale mean of 0.5 in as a substitute to avoid unwanted discrimination. 4.3.4 Principal’s Preference Information The preference information required for running the scenario comprises a weight vector with values for each attribute. At the beginning the principal is interrogated to elicit his preference structure on price, image and social reputation. The interview produces a criteria comparison table (cf. Subsection 3.2.3) and calculates the following results (Table 18): Table 18: Weight vector PR IM SR Sum Weight PR 1 1/2 3/4 2.25 wPR = 0.23 = 23 % IM 2 1 3/2 4.5 wIM = 0.46 = 46 % SR 4/3 2/3 1 3 wSR = 0.31 = 31 % Sum 9.75 100 % j w=  During our experiment we assume these weights are constant and are not subject to manipulation, neither by the principal nor by the agent. 77 4.4 The Extended TOPSIS 4.4.1 Description of the Technique The TOPSIS creates every time two virtual bounds against which all alternatives are ranked (cf. Subsection 3.3.5.4, p. 53). This feature is helpful when tracking past selections and comparing them in the course of time. The two bounds incorporate the extreme values for attributes of all received alternatives so far, thus, it serves as a “packed memory” one may consult when ranking the previously selected alternatives. A ranking of selected alternatives (a “best-of-the-best list”) allows assessments of the past performance of the buyer agent, e.g. analyzing whether specific hubs provide frequently malevolent sellers or specific periods when demanded prices are unusually low. This cannot be achieved easily by applying MCDM methods such as the WPM or the SAW method because those methods mask all but their synthesized score value (cf. Subsection 3.3.5.2, p. 45). We propose an Extended TOPSIS (xTOPSIS) approach here, which computes the two bounds over the course of time instead of resetting the ideal solution vectors after every instance. This means, after their first construction, the two vectors with the ideal solution are reverted into their original values and added to the set of alternatives every run before carrying out the TOPSIS procedure (Figure 37). We call these two extreme points negative and positive ideal vector. In order to apply this line of action we replace the vector normalization with the linear one as accomplished before by [YuCo03, 1000], [Chu02, 695]. The linear transformation requires merely two extreme values for scaling – and these parameters are given at any time by the two ideal vectors. Furthermore, we need to store three vectors after every run: First of all, the positive and negative ideal vectors are saved in a database, namely the Ideal Vector Database (IVD). Besides we establish a Partner Database (PD) consisting of all offers the agent successfully seized. With the help of these two storages, we can align attribute values of alternatives on a single scale and compare them to each other. 84 4.5.2 Seller Evaluation Seller evaluation is not automated in the process of the scenario. The quality of the storage provided cannot be determined by the buying agent, thus the principal is currently supposed to interact with the ALN and provide a feedback for the individual and the collective memory (the ODB and the current hub’s IDB and SDB). At this stage, the interactivity requirement is a bottleneck for large-scale applications since it impeds the process (cf. p. 68). To avoid this, we suggest the implementation of a yet unspecified automatism for evaluations. 4.5.3 Summary Synthesizing the result from the comparison of eleven MCDM approaches with the prerequisites of the environment has led to three possible options: SAW, WPM and TOPSIS. We have chosen the latter since we saw the chance to derive additional benefit from the provision of extreme vectors compared to plain score values. Instead of estimating new reference vectors for each buying request, we store all references in a repository and adapt the two current ideal solutions during each run. Thus, we can judge all alternatives by two dynamic reference vectors, and we determine the value of an offer not merely at a certain time, but also over several periods. With regard to this extension we have baptized the approach xTOPSIS. The method is scalable and suitable for the given premises, and thus practical for large-scale analysis. Moreover, it provides an interface for monitoring the quality of past transactions as it creates a set of two vectors per transaction, which can be either used in overarching research on system performance or become subject of trade as well. A drawback worth noting is the missing implementation of automated outcome evaluation. Since this problem is beyond our objective of defining a suitable MCDM method, we have not examined possible solutions. 85 5 Conclusion 5.1 Results We have examined decision-making in ALN and concentrated on the case of processing reputation information during the purchase of goods. To automate the reasoning process of agents before selecting a supplier, we have analyzed the environment and extracted aspects of relevance for a suitable MCDM method. The primary objective of this work was the elaboration of a suitable decision-making method for the simulation testbed of the eRep project. We deduced an approach called xTOPSIS from the prerequisites of the testbed, elaborated the foundations and presented a numerical example to illustrate the process. Thus the objective has been achieved. In view of the secondary objectives we are able to answer the questions  whether the chosen decision-making method can be applied to the trade of services and complex goods,  which assumptions of the scenario impede transferring the results to human environments, and  whether valuable added benefits can be drawn from the used method. Trading Services Shifting from commodities to complex goods or services means a soaring number of distinguishing features, i.e. an increase of criteria. Thus the number of processing operations rises: on the one hand because of additional preference information the agent needs from the principal, and on the other hand because of the size of the information requested from the hub. For the xTOPSIS this implies growing IVD and PD repositories and a growing number of computations. Technically, the xTOPSIS is able to deal with the requirements of service procurement, but practically, one may question whether the TOPSIS philosophy is suitable for service procurement: In contrast to reputation, suppliers may be in the position of adjusting services attributes or balancing weaknesses in negotiation processes. Upon revealing a value function, buyers and seller are able to engage in multiattribute auc- 86 tion mechanisms which may be more helpful in this case [Bich01, 140–144]. Impeding Assumptions During our elaboration several concessions had to be made in order to allow an efficient scenario modeling. Among those, the four aspects below seem most critical when it comes to transferring the results from the project to real life situations. Although the purpose of this work has never been imposing a formal mechanism on real life social structures, when planing to establish an appealing and plausible eCommerce governance environment, we have to remind ourselves to the fact that the consumers sitting in front of computer screens are (still) human beings. 1. Constant weights: We can hardly imagine human beings attribute the same relevance to criteria in the long run. People rather adapt constantly and change preferences upon experiences. If weights are to be parameterized, then an additional Weights Database would have to be implemented to trace the change of relative preferences. The same applies to any measure implemented for enabling automated seller evaluation. 2. Learning: Currently, neither the seller nor the buyer agent reflect on past actions and improve their behavior. Assuming an automated evaluation mechanism exists, the buyer is supposed to consider the outcome of his conduct and adapt to the results. One idea might be excluding specific hubs or periods which provided less valuable bargains. This would be equal to a human being avoiding particular shopping malls or opening hours in which she was previously not satisfied by her transaction. 3. Voluntary information dissemination: The ReGreT mechanism relies on provided feedback from customers to compute the social reputation value. It is questionable whether individuals provide word-of-mouth for free, assuming transaction cost are inevitable. For example, one may consider implementing a deposit for retrieved reputation information, which is returned upon submitting feedback, or a market mechanism encouraging individuals to trade honest feedback. 4. Additive value function: Additive partial value functions are inherent in the TOPSIS approaches. But even in the regarded scenario, the necessary precon- 87 dition of mutual independence between those functions is violated – social reputation is slightly influenced by the image of an agent, if he previously met the regarded seller. In everyday life interdependencies between attributes such as reputation and price are also very likely. One thought may be considering nonlinear value functions such as the multiplicative one of the WPM. This list of four obstacles is by no means extensive, and the nature of models such as the ReGreT mechanism suggest sources of conflict at every stage of abstraction; we briefly refer to the design of sociograms or the individual adaptations to the ontological dimension for calculating trust (cf. Subsection 2.5.2.3, p. 22). Added benefits Thanks to retaining previous ideal vectors (in the IVD) and seized offers (in the PD), the xTOPSIS allows intertemporal comparisons of reached agreements and ideal solutions. This means, for one thing we can analyze time series of temporary offer markets, for another one we can observe the performance of our agent. The ideal vectors embody certain market states, since they comprise the extreme values of all alternatives on the market. Assuming time stamps and identity of the connecting hub are available as well, the data from the IVD can provide grounds for metrics such as average offer quality or correlation between price and reputation (in relation to periods or hubs). It furthermore allows enhancements for the reasoning process of an agent, e.g. computing thresholds, aspiration levels, or reservation values in reference to the previously encountered markets. If a threshold is not reached, the agent can be instructed to react with sanctions such as switching the hub or rejecting all offers. The database with past encounters enables tracing the performance of an agent; scaling all previous deals with respect to one set of ideal vectors makes the results comparable. We can see which offers were above or below average, and if we connect the results with the evaluations from the ODB, we can try to define patterns of good and not-so-good suppliers, e.g. we may find out that reputation is a good predictor of quality for offers from certain hubs. One can imagine the possibilities of analyzing past encounters and deriving predictions for future trading. Conducting data mining is possible with other value function methods as well, but the crucial disadvantage of SAW or WPM is the necessity to 88 store all received offers with their attributes. In contrast, the TOPSIS approach supports our suggested extension in terms of efficiency. 5.2 Suggestions for Research and some Critical Annotations During the development of our method several matters of interest arose, which we had to postpone until now. For the field of MCDM in ALNs, we reduce our suggestions for further research to the following issues:  How can we delegate the process of evaluating outcomes to an agent?  What constitutes the border between those goods for which we can apply MADM methods and those goods for which we need other approaches?  To what extent are human beings willing to transfer responsibility to agents? Evaluating outcomes Currently, the whole subprocess of learning has not been specified. Learning itself is a problematic issue already mentioned above, but part of it includes the evaluation of outcomes. Processing some rough information can be realized through comparing certain service level measures to specified, individual target values (such as medium access time, latency or access availability). But in terms of less easily quantifiable measures, how shall an agent derive an evaluation? Consider streaming a movie from a provider – though possible from a technical point, but hardly computable, how shall the buying agent estimate the quality of the movie? How shall he detect visual or acoustic differences on time, assuming all files use the same audio and video encoder? This certainly asks for further research on mechanisms for delegating parts of the evaluation to agents. Limitations of MADM methods for comparable goods The elaborated method is sufficient for the straightforward comparison of commodity sellers. Beyond attribute-free goods, when it comes to more complex ones or services, information on the type of distinguishing features is necessary. Whereas the comparison of identical music files offered may come up with a few additional numerical attributes (such as the encoding bitrate), service providers offering PDF conversions 89 may present a whole variety of encryption techniques, compression algorithms, or size restrictions. Thus, further investigations are required to determine the limitations of MADM methods for comparing goods with multiple attributes. Limits for transferring responsibility Above the technical aspects, we need to ask ourselves in how far we want to delegate decision-making to autonomous agents. True, agents possess the ability to facilitate daily life by exchanging information and conducting trades of minor importance on behalf of the principals. But for privacy as well as self-determination matters, it is questionable whether individuals are willing to provide comprehensive information on their preference structure to their non-human alter ego, even if we take exhaustive security measures against abuse. The individual concern for privacy protection leads to questions regarding already institutionalized rules [Seif86, 35–36]: The replication of preference structures and transaction histories severely violates individuals’ privacy. Storing personal information in distributed repositories appears to interfere in several facets such as the right for privacy and self-determination with the EC Directive on privacy and electronic communications, e.g. Articles 5, 12 Directive 2002/58/EC [Euro02b], [Seif86, 38]. Moreover, assuming agents take on more or less all transactions between individuals, we may end up asking ourselves whether trading is not a common part of human behavior. Are we willing to forgo this habit? And can the human mind ever be appropriately represented by an autonomous device – or will we have to adapt our capacious human minds gradually to the limits of artificially empowered assistants [Lani96]? If we agree on the ideas of digitalizing the human mind as well as forgoing the human habit of trading, the giving up of buying and selling provokes a decline of individual socializing [Seif86, 11]. 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Springer: Berlin, Heidelberg, New York, 1991. 105 Appendix Appendix A Appendix A 1: Classification categories and options (based on [SaSi05, 35–41]) Conceptual model GT Game-theory C Cognitive Information sources DI Direct interaction DO Direct observation WI Witness information SI Sociological information P Prejudice Visibility S Subjective property G Global property Model’s granularity CD Context dependent NCD Noncontext dependent Agent behavior assumptions 0 No cheating is considered 1 Biased or hidden information possible 2 Lying is recognized Type of exchanged information Yes / No Boolean measures Trust/reputation reliability measure Yes / No Available 106 Appendix A 2: Comparison of reputation systems [SaSi05, 56] Conceptual model Information source Visibility Model’s granularity Agent behavior assumptions Boolean exchanged information Trust-Rep reliability measure Model type S. Marsh GT DI S CD NAa NAa No Trust Online Rep models GT WI G NCD 0 No Nob Rep Sporas GT WI G NCD 0 No Yes Rep Histos GT DI+WIc S NCD 0 No No Rep Schillo et al. GT DI, DO, WI S NCD 1 Yes No Trust A.-Rahman and Hailes GT DI, WId S CD 2 4 trust values No Trust Rep Esfandiary and Chandrasaekharan GT DI, DO, WI, P S CD 0 No No Trust Yu and Singh GT DI, WI S NCD 0 No No Trust Rep Sen and Sajja GT DI, DO, WIe S NCD 2f Yes No Rep AFRAS GT DI+WIc S NCD 2 No Yes Rep Carter et al. GT WIg G NCD 0 No No Rep Castelfranchi and Falcone C NAh S CD NAh No NAh Trust ReGreT GT DI+WI+SI+Pc S CD 2 No Yes Trust Rep a b c d e f g h There is no exchange of information between agents. Reliability is based on the number of ratings. The ’+’ symbol means the model combines the information sources to obtain a final trust/reputation value. Direct experiences are used to compare the point of view of these witnesses with the direct perception of the agent and then be able to adjust the information coming from them accordingly. Because the objective of this work was to study how agents use word-of-mouth reputations to select on of several partners, agents only use witness information to take decisions. Liars are assumed to lie consistently. Besides information coming from other users (WI) there is a central authority that monitors the agents’ behavior and uses that information to build reputation. In the description of the model it is not specified how the agents obtain the information to build their beliefs. 107 Appendix A 3: Main process of buying storage capacity with xTOPSIS Main process: Buying storage capacity with xTOPSIS auction won? [yes] Place bid Place bid Information on offer and dealer Information on offer and dealer Request offer and dealer information Request offer and dealer information Learning Learning Preference information Preference information Positive and negative Ideal vector Positive and negative Ideal vector Find new offer Find new offer Demand detected Demand detected Learning Learning Preference information Preference information Positive and negative Ideal vector Positive and negative Ideal vector [no] Select topranked alternative Select topranked alternative Ranking Ranking Alternative Alternative xTOPSIS xTOPSIS Main process: Buying storage capacity with xTOPSIS auction won? [yes] Place bid Place bid Information on offer and dealer Information on offer and dealer Request offer and dealer information Request offer and dealer information Learning Learning Learning Learning Learning Learning Preference information Preference information Positive and negative Ideal vector Positive and negative Ideal vector Find new offer Find new offer Demand detected Demand detected Demand detected Demand detected Learning Learning Learning Learning Learning Learning Preference information Preference information Positive and negative Ideal vector Positive and negative Ideal vector [no] Select topranked alternative Select topranked alternative Ranking Ranking Alternative Alternative xTOPSIS xTOPSIS xTOPSIS xTOPSIS 108 Appendix B: Case Study Situation Our DM, a new entrant in a sales company, is supposed to pick a brandnew middle class car from a list of seven alternatives. He decides on the basis of five criteria, in which all alternatives differ from each other (Appendix B 1).1 Non-discriminating criteria in which all alternatives are equal or very similar, are disregarded2; such aspects include the required petrol standard, 95 RON3 (Eurosuper), the emission level (EURO IV), and the Euro NCAP safety assessment (all cars have been rated with five stars). With exception of the trunk volume, all data is based on manufacturer information drawn from technical specifications on the respective German website. Since trunk volume appears to differ in the norms of measuring, data from recent tests of the ADAC, the General German Automobile Association, is taken into consideration. Despite the difference of their units, all dimensions are scaled on a ratio level. Appendix B 1: Criteria in the car comparison Price Fuel consumption Carbon dioxide emission Acceleration Trunk volume Criterion Manufacturer’s list price in Germany 95 RON Eurosuper, combined (in town, out of town) Combined (in town, out of town) Acceleration (from 0 to 100 kmph) Storage volume of the trunk, without folded seats EUR Ltr/100km g/km sec Ltr Unit measured Euros Liters per 100 kilometer Grams per kilometer Seconds Liter Source Manufacturer websites ADAC Goal Minimize Minimize Minimize Minimize Maximize The set of alternatives includes seven models of different brands which have been chosen in accordance with a similar target market segment; in terms of premium 1 Similar problems with different criteria and alternatives are presented by [BMP+00, 91–93], [YoHw95, 24]. 2 Engine power was disregarded because in the set of alternatives it correlated strongly with acceleration (correlation coefficient of 0.7932). 3 Research Octane Number 109 brands this may be disputed, but since the Ford’s basic price exceeds the prices of the Alfa Romeo, the Audi A4, the Saab 9-3 and the Volvo S40, we included the Mondeo. Appendix B 2: Car selection and information sources Source of information Brand Model All data (except trunk volume) Trunk volume Alfa Romeo 159 1.8 MPI 16V [Fiat08, 3], [Fiat08, 16-17] [Thyw05c, 4] Audi A4 Attraction 1.8TFSI [Audi08a, 4], [Audi08b] [Sipp08, 6] BMW 318i [BMW08a, 3], [BMW08b, 23-24] [Thyw05a p. 4] Ford Mondeo Ghia 2.0l [Ford07, 29], [Ford08, 4] [Ruhd07a, 5] Mercedes C180 Kompressor [Daim07, 2], [Daim08, 5] [Ruhd07b, 6] Saab 9-3 1.8i M5 [Saab07, 3], [Saab08] [Thyw04b, 4] Volvo S40 1.6 [Volv08a, 3], [Volvo08b] [Thyw04a, 4] All cars are four doors, sedan body style (though in case of the Ford Mondeo, the sedan is more expensive than the station wagon) and basic editions with manual transmission, in order to be competitive as well as comparable in all criteria (Appendix B 2). Decision matrix The decision matrix in its initial appearance is presented below (Appendix B 3). Appendix B 3: Initial decision matrix for car purchase Price Fuel consumption Carbon dioxide emission Acceleration (0-100 kmph) Trunk volume Brand Model EUR Ltr/100 km g/km sec Ltr Alfa Romeo 159 1.8 MPI 16V 24,550 7.6 179 10.2 445 Audi A4 Attraction 1.8TFSI 25,900 7.1 169 10.5 380 BMW 318i 27,300 7.9 142 9.1 405 Ford Mondeo Ghia 2.0l 26,000 7.9 189 9.9 515 Mercedes C180 Kompressor 31,089 7.6 177 9.5 350 Saab 9-3 1.8i M5 25,650 7.7 183 11.5 440 Volvo S40 1.6 21,450 7.2 171 11.9 404 We will later apply MCDM methods which require normalized attributes. For this 116 () () 1 j nw j j VA v  = = with max j i j vv = () () ()( ) ()      ! ! "" ## = "" ## "" ## $%$%  0,2 0,09 0,3 0,24 0,17 Ltr g 21,450 EUR 7.1 142 9.1 sec 515 Ltr 100 km km 0.05744 VA VA Third step: Now we get the score for the Alfa taking the ratio of VAlfa and V(A*), () = 0.05164 0.899 0.05744 Alfa V VA . Appendix B 13: Weighted Product Method Price Fuel consumption Carbon dioxide emission Acceleration (0-100 kmph) Trunk volume Brand Model EUR Ltr/100 km g/km sec Ltr Score () i V VA  Alfa Romeo 159 1.8 MPI 16V 0.04819 0.66656 0.99534 0.57271 2.81982 0.899 Audi A4 Attraction 1.8TFSI 0.04743 0.67569 0.99539 0.56874 2.74513 0.867 BMW 318i 0.04668 0.66142 0.99555 0.58861 2.77503 0.8741 Ford Ghia 2.0l 0.04737 0.66142 0.99529 0.57683 2.89073 0.9053 Mercedes C180 Kompressor 0.0449 0.66656 0.99535 0.58257 2.70702 0.8178 Saab 9-3 1.8i M5 0.04756 0.66482 0.99532 0.55646 2.81441 0.8581 Volvo S40 1.6 0.05018 0.6738 0.99538 0.55191 2.77386 0.8971 Although both methods use the same weights, they produce different results when it comes to the final recommendation: the SAW prefers the Volvo, the WPM suggests the Ford. This stems from the normalization methods – being the weakest choice in fuel consumption and carbon dioxide emission, the Ford’s outcome on these dimensions is set to zero in the SAW method; one strength (trunk) cannot compensate for 117 these two flaws. The Volvo in contrast has to cope with only one relatively weak attribute (acceleration). Analytic Hierarchy Process Now we examine the course of action for the Analytic Hierarchy Process. First, we depict the decision situation in a hierarchy with three levels. The superior goal weights vector consists of the elicited relative contributions of each criterion for the overall goal. We take our weights vector (Appendix B 11, p. 114) and assume it is based on pairwise comparisons; then we attach the weight values to their respective edge, highlighted in red color (Appendix B 14). Appendix B 14: Hierarchy for the AHP method (A1) Alfa Romeo 159 (A2) Audi A4 (A3) BMW 318i (A4) Ford Mondeo (A5) Mercedes C180 (A6) Saab 9-3 (A7) Volvo S40 A1 A2 A3 A4 A5 A6 A7 PR FU CO AC TV (PR) Price (FU) Fuel consumption (CO) Carbon dioxide emission (AC) Acceleration (TV) Trunk volume Level 1: Goal Level 2: Criteria Level 4: Alternatives 0.3 0.2 0.09 0.24 0.17 (A1) Alfa Romeo 159 (A2) Audi A4 (A3) BMW 318i (A4) Ford Mondeo (A5) Mercedes C180 (A6) Saab 9-3 (A7) Volvo S40 A1 A2 A3 A4 A5 A6 A7A1A1 A2A2 A3A3 A4A4 A5A5 A6A6 A7A7 PR FU CO AC TVPRPR FUFU COCO ACAC TVTV (PR) Price (FU) Fuel consumption (CO) Carbon dioxide emission (AC) Acceleration (TV) Trunk volume Level 1: Goal Level 2: Criteria Level 4: Alternatives 0.3 0.2 0.09 0.24 0.17 Secondly, we calculate the five weight vectors for the five criteria (which correspond with blue edges between the level 2 and level 3 nodes). A vector is determined by comparing pairwise the alternatives with regard to the respective criterion, e.g. how many times is the price of the Alfa better than the price of the Audi, and by calculating the geometric mean for each alternative afterwards4. This means we have three steps for each criterion: 1. Constructing a pairwise comparison matrix, 2. calculating geometric means for each alternative, and 3. applying a linear transformation to normalize the means into a weights vector (Appendix B 15, where these weights are highlighted in red). 4 Although Saaty recommends the use of his eigenvector method, we use the simpler geometric mean calculation here and omit the consistency check. 118 The other four vectors are given for further calculation and are not explicitly derived here (Appendix B 16). Appendix B 15: The pairwise comparison matrix and the weight vector for the price criterion 1 5 9 5 7 5 3 A7 1/51 5 1 1 1 1 A6 1/91/51 1/51/31/51/7 A5 1/51 5 1 1 1 1 A4 1/71 3 1 1 1 1/3 A3 1/51 5 1 1 1 1 A2 1/31 7 1 3 1 1 A1 A7A6A5A4A3A2A1 1 5 9 5 7 5 3 A7 1/51 5 1 1 1 1 A6 1/91/51 1/51/31/51/7 A5 1/51 5 1 1 1 1 A4 1/71 3 1 1 1 1/3 A3 1/51 5 1 1 1 1 A2 1/31 7 1 3 1 1 A1 A7A6A5A4A3A2A1 Step 1 Step 1 9.52975 6 0.442274.21471 A7 0.104931 A6 0.024900.23726 A5 0.104931 A4 0.079470.75731 A3 0.104931 A2 0.138561.32047 A1 Normalized weight Geom. Mean 9.52975 6 0.442274.21471 A7 0.104931 A6 0.024900.23726 A5 0.104931 A4 0.079470.75731 A3 0.104931 A2 0.138561.32047 A1 Normalized weight Geom. Mean PRPR Step 2 Step 2 Step 3 Step 3 Finally, the resulting five (7x1)-vectors display the relative contribution of each car with regard to the specific criterion; we can merge these five columns into a (7x5) matrix. This comes in handy for determining the composite values, because we can easily multiply this matrix with the goal vector for the five criteria (Appendix B 16). Appendix B 16: Weight vectors for all five criteria Normalized weights Brand PR FU CO AC TV Goal weights Score i V Alfa Romeo 0.1385 6 0.07269 0.07424 0.12399 0.16212 0.12011 Audi 0.1049 0.38069 0.13417 0.08729 0.0467 0.3 0.14858 BMW 0.0794 0.02942 0.51336 0.31794 0.06092 0.2 0.16259 Ford 0.1049 0.02942 0.03554 0.16971 0.48692 u 0.09 = 0.16407 Mercedes 0.0249 0.07269 0.08685 0.24372 0.03172 0.24 0.09371 Saab 0.1049 0.06928 0.05424 0.03161 0.15071 0.17 0.0834 Volvo 0.4422 0.3458 0.10161 0.02575 0.06092 0.2275 6 (column) 1 1 1 1 1 1 1 119 We receive the five score values by conducting the matrix multiplication as mentioned. Say, for the Alfa Romeo one can compute the score value VAlfa by adding the Alfa’s criteria contributions weighted with goal weights already given as follows: ()()( )( )( ) =++++     1 PR contribution FU contribution CO contribution AC contribution TV contribution 0.13856 0.3 0.07269 0.2 0.07424 0.09 0.12399 0.24 0.16212 0.17V   10.12V Thus, with a score value of () = 70.228VA the Volvo emerges as the best choice. This is the same result as in the SAW method, due to the similarity of both methods in summarizing the partial values: The relative contributions of the AHP can be compared to the absolute values of the SAW method. Technique for Order Preference by Similarity to Ideal Solution We start with normalizing the decision matrix, but this time, we make use of the vector transformation which will lead to results different from the linear one (Appendix B 17). Appendix B 17: Vector normalized decision matrix Brand Model Price Fuel consumption Carbon dioxide emission Acceleration (0-100 kmph) Trunk volume Alfa Romeo 159 1.8 MPI 16V 0.39380 0.37569 0.36077 0.37971 0.39786 Audi A4 1.8TFSI 0.37328 0.40214 0.38212 0.36886 0.33975 BMW 318i 0.35413 0.36142 0.45478 0.42561 0.36210 Ford Ghia 2.0l 0.37184 0.36142 0.34168 0.39122 0.46045 Mercedes C180 Komp. 0.31097 0.37569 0.36485 0.40769 0.31293 Saab 9-3 1.8i M5 0.37691 0.37081 0.35289 0.33679 0.39339 Volvo S40 1.6 0.45071 0.39656 0.37765 0.32547 0.36121 Continuing with weighting the results, we hold on to the same trade-off values as used before in SAW, WPM and AHP (Appendix B 11, p. 114). Thus, we receive a matrix with weighted normalized values (Appendix B 18). 120 Appendix B 18: Weighted normalized decision matrix Brand Model Price Fuel consumption Carbon dioxide emission Acceleration (0-100 kmph) Trunk volume Alfa Romeo 159 1.8 MPI 16V 0.11814 0.07514 0.03247 0.09113 0.06764 Audi A4 1.8TFSI 0.11198 0.08043 0.03439 0.08853 0.05776 BMW 318i 0.10624 0.07228 0.04093 0.10215 0.06156 Ford Ghia 2.0l 0.11155 0.07228 0.03075 0.09389 0.07828 Mercedes C180 Komp. 0.09329 0.07514 0.03284 0.09785 0.05320 Saab 9-3 1.8i M5 0.11307 0.07416 0.03176 0.08083 0.06688 Volvo S40 1.6 0.13521 0.07931 0.03399 0.07811 0.06140 Again, best (and worst) values are highlighted in blue (red) – those values comprise the positive (negative) ideal solution in the next step. Thus, we receive the following two vectors (Appendix B 19). These two vectors span a convex set of alternatives among which our seven cars are located. Appendix B 19: Positive and negative ideal solution Reference point Price Fuel consumption Carbon dioxide emission Acceleration (0-100 kmph) Trunk volume Positive ideal solution 0.13521 0.08043 0.04093 0.10215 0.07828 Negative ideal solution 0.09329 0.07228 0.03075 0.07811 0.05320 To determine the final ranking, we calculate separation measures S+i (S-i) for each alternative to these reference points. We retrieve the closeness of the Alfa Romeo to the positive ideal solution from () ()( ) ()( )( )()() = ++ =  ==++ =  + + + +   ! 5222 1 22222 0.11814 0.13521 0.06764 0.07828 0.01707 0.00529 0.00846 0.01102 0.01064 0.02501 0.03172 n Alfa j Alfa j j j j Alfa Swvwv S and compute the similarity measure RAlfa with 121  + ==  ++ 0.03172 0.55916 0.02501 0.03172 Alfa Alfa Alfa Alfa S RSS . Sorting the alternatives according to the similarity measure, we get a ranking with a clear recommendation for the Volvo – and the good advice not to consider the Mercedes any further (Appendix B 20). Regarding the closeness indices, we see that the Alfa is in absolute terms closer to the positive ideal solution, but – due to some criteria values – also closer to the negative ideal one. The Volvo beats the Alfa because of compensating for the lack of excellence in acceleration with possessing relatively strong figures in terms of price and fuel consumption. This indicates the similarity between the SAW and TOPSIS (i.e. the additive compensation between criteria). Appendix B 20: Similarity to positive ideal solution Closeness to… Brand Model positive ideal solution negative ideal solution Similarity Rank Alfa Romeo 159 1.8 MPI 16V 0.02501 0.03173 0.55916 2 Audi A4 1.8TFSI 0.03448 0.02363 0.40659 6 BMW 318i 0.03443 0.03031 0.4682 4 Ford Ghia 2.0l 0.02825 0.03481 0.55199 3 Mercedes C180 Komp. 0.04998 0.02005 0.28626 7 Saab 9-3 1.8i M5 0.03461 0.0243 0.41246 5 Volvo S40 1.6 0.03019 0.04341 0.58979 1 Finally, we need to come back to the normalization mechanism: The choice of the technique exerts influence on the final ranking order; if we had applied the linear normalization, the Audi for instance would have come out much better and the winner would have been the Alfa (Appendix B 21). Thus, a sensitivity analysis is compulsory to make an entirely satisfactory decision. 122 Appendix B 21: Similarity and Ranking for linear normalization Brand Model Similarity Rank Alfa Romeo 159 1.8 MPI 16V 0.57131 1 Audi A4 1.8TFSI Attraction 0.54977 3 BMW 318i 0.49529 5 Ford Ghia 2.0l 0.51685 4 Mercedes C180 Kompressor 0.37028 7 Saab 9-3 1.8i M5 0.39788 6 Volvo S40 1.6 0.56443 2 ELECTRE Last, we use an outranking technique to see if we can elicit a distinct recommendation for our case. Because it is common practice to use a decision matrix with vector normalized values and since we assume the same weights as before (Appendix B 11, p. 114), we start with the weighted normalized decision matrix as in the TOPSIS description (Appendix B 18, p. 120). On the grounds of this information we use the outranking relation S and elicit the concordance indices to assess the strength of support for the statement that one car outranks another. With () {} :kj lj kl k l j ja a con con A SA w  ==  with {} ,1,,7kl k l! , we receive for the outranking relation AAlfaSAAudi that the Alfa 159 excels the Audi A4 in price, acceleration and trunk volume. The concordance index of the statement that the Alfa is better than the Audi is equal to the sum of the corresponding weights, thus 0.71 (wprice= 30 %, wacceleration= 24 %, wtrunk_volume= 17 %). After 7 × 6 = 42 comparisons (outranking relations are not reflexive), we obtain the complete matrix with concordance indices (Appendix B 22). 123 Appendix B 22: Concordance indices Alfa Romeo Audi BMW Ford Mercedes Saab Volvo Alfa Romeo 0.71 0.67 0.59 0.67 1 0.41 Audi 0.29 0.5 0.59 0.83 0.53 0.53 BMW 0.33 0.5 0.53 0.8 0.33 0.5 Ford 0.41 0.41 0.67 0.47 0.41 0.41 Mercedes 0.53 0.24 0.2 0.53 0.53 0.24 Saab 0 0.47 0.67 0.59 0.47 0.41 Volvo 0.59 0.47 0.5 0.59 0.76 0.59 Afterwards we turn to the discordance indices, the strength of dissent on the statement that one car outranks another. With () {} : max max kj lj jkj jlj ja a kl k l jkj jlj j wa wa dis dis A SA wa wa < ==  with {} ,1,,kl m k l!. we compute the strength of discordance for statement that the Alfa outranks the Audi in two steps. First, with regard to the nominator of the fraction, we estimate the maximum difference on weighted normalized values between the two cars from the subset of criteria in which the Alfa is not outdoing the Audi, fuel consumption and carbon dioxide emission: {} () () : max max 0.07514 0.08043 ; 0.03247 0.03439 max 0.00529; 0.00192 0.00529 Alfa j Audi j jAlfaj jAudij ja a wa wa < =   == In the second step, the denominator, which is equivalent to a scale coefficient, is computed from the maximum difference on weighted normalized values between the two cars on all criteria: 124 ( ) () max 0.11814 0.11198 ; 0.07514 0.08043 ; 0.03247 0.03439 ; 0.09113 0.08853 ; 0.06764 0.05776 0.00616; 0.00529; 0.00192; 0.0026; 0.00988 0.00988 jAlfaj jAudij jwa wa =    = = Repeating these two steps for all 42 matrix entries, we determine the matrix with discordance indices (Appendix B 23). Appendix B 23: Discordance indices Alfa Romeo Audi BMW Ford Mercedes Saab Volvo Alfa Romeo 0.53559 0.92565 1 0.27023 0 1 Audi 1 1 1 0.49857 1 1 BMW 1 0.59801 1 0.22037 0.32059 1 Ford 0.61926 0.39693 0.60878 0.15764 0.14372 1 Mercedes 1 1 1 1 1 1 Saab 1 0.84412 1 1 0.8602 1 Volvo 0.76249 0.4483 0.8295 0.71299 0.47071 0.24714 To qualify the concordance and discordance values, we will now continue with building the concordance dominance matrix mm× F\ and the discordance dominance matrix mm× G\. Therefore we compute the arithmetic mean of each matrix as a threshold value – if a matrix entry is below the threshold, we assume the statement is too weak to be taken seriously. With the mean values =0.51119con ( =0.7493dis ) for the concordance (discordance) indices we receive the concordance dominance matrix (Appendix B 24) and the discordance dominance matrix (Appendix B 25). 125 Appendix B 24: Concordance dominance matrix Alfa Romeo Audi BMW Ford Mercedes Saab Volvo Alfa Romeo 1 1 1 1 1 0 Audi 0 0 1 1 1 1 BMW 0 0 1 1 0 0 Ford 0 0 1 0 0 0 Mercedes 1 0 0 1 1 0 Saab 0 0 1 1 0 0 Volvo 1 0 0 1 1 1 Appendix B 25: Discordance dominance matrix Alfa Romeo Audi BMW Ford Mercedes Saab Volvo Alfa Romeo 1 0 0 1 1 0 Audi 0 0 0 1 0 0 BMW 0 1 0 1 1 0 Ford 1 1 1 1 1 0 Mercedes 0 0 0 0 0 0 Saab 0 0 0 0 0 0 Volvo 0 1 0 1 1 1 Finally, we aggregate the two matrices into a dominance matrix, which can be understood as a table with measures indicating that the outranking statement between two cars is supported and not rejected or vice versa (Appendix B 26). We read this table row-wise and eliminate all cars in columns where the pivotal entry is a one, namely the Audi, the BMW, the Ford, the Mercedes and the Saab. Regarding the remaining two models, we cannot distinguish between them: the Alfa Romeo and the Volvo are “incomparable” and thus of equal value to the DM.