Sustainability performance assessment of industrial corporation using Fuzzy Analytic Network Process

Sustainability performance assessment of industrial corporation using Fuzzy Analytic Network Process Pavel Wicher a , Franti sek Zapletal b , * , Radim Lenort a a V SB - Technical University of Ostrava, Faculty of Materials Science and Technology, 17. Listopadu 2172/15, Ostrava, 70800, Czech Republic b V SB - Technical University of Ostrava, Faculty of Economics, Sokolsk a 33, Ostrava, 70200, Czech Republic article info Article history: Received 11 January 2019 Received in revised form 3 July 2019 Accepted 21 August 2019 Available online 3 September 2019 Handling editor: Dr. Govindan Kannan Keywords: Sustainability performance assessment Aggregated assessment Methodology Fuzzy analytic network process Multi criteria decision making Metallurgy abstract Nowadays, sustainability is one of the leading value-increasing strategies of industrial corporations. In order to implement a sustainable strategy, it is necessary to assess the sustainability performance. Nevertheless, this still represents a relevant gap in the literature and practice. There are a number of frameworks and tools for sustainability performance assessment. Most of them are based on a set of indicators. However, in many corporations the sets are applied and kept disaggregated. Due to this deficiency, aggregated sustainability assessment approaches are often explored by researchers and practitioners. One of the main approaches is the use of multi criteria decision making methods which transform multiple indicator values to a single dimension. Since there are many complex interdependencies among the used sustainability key performance indicators and their relations are uncertain, Fuzzy Analytic Network Process (FANP) appears to be an appropriate tool for aggregated assessing the sustainability performance. The aim of this paper is to develop and verify a methodology for aggregated sustainability performance assessment of an industrial corporation using the FANP approach. Based on analysis of the existing FANP approaches and discussion of their advantages and disadvantages, Logarithmic Fuzzy Preference Programming Methodology was selected for this purpose. Our developed methodology provides a comprehensive aggregated sustainability performance assessment system based on combining three evaluation methods (basic evaluation, trend evaluation, and categorization), and Action matrix, which defines appropriate corrective actions level to achieve the sustainability performance targets. A case study from metallurgical industry was used to verify the developed methodology and to identify critical points and recommendations for its implementation. ©2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction Sustainability has been more and more in focus during the last years, both among the corporations and researchers. Nowadays, this concept becomes the key strategy of most industrial corporations. In order to implement the strategy, it is necessary to have effective sustainability performance assessment system. Although there are many frameworks and tools for assessing sustainability performance in the literature, none of them offers a comprehensive and aggregate way to assess the sustainability performance. Also, in corporate practice, the assessment of sustainability performance faces methodological problems. The sustainability performance is presented in sustainability reports elaborated according to various international sustainability standards. Our analysis of industrial leaders’sustainability reports (such as Volkswagen, Toyota in automotive industry or ArcelorMittal, POSCO in metallurgical industry) enables to characterise main features of the sustainability performance assessment. Industry leaders use a set of key performance indicators (KPIs) to measure the sustainability, in order to evaluate and monitor the KPIs annually. However, the reports do not contain any comparison with strategic target or threshold KPIs values, and provide only disaggregated assessment of the sustainability performance. The disaggregated assessment means that measured KPIs are evaluated separately, without their interdependencies and holistic view on the corporate sustainability performance. The aggregation allows to combine a diverse range of economic, environmental and social KPIs and their units and to provide a meaningful and interpretable result for assessing the overall development of the corporate *Corresponding author. E-mail addresses: [email protected] (F. Zapletal), [email protected] (R. Lenort). Contents lists available at ScienceDirect Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro https://doi.org/10.1016/j.jclepro.2019.118132 0959-6526/©2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Journal of Cleaner Production 241 (2019) 118132 sustainability. Such information is needed not only for the corporate top management, but also for all its stakeholders. The above shortcomings of current approaches to the sustainability performance assessment still reveal a relevant gap in research and practice and evoke an urgent need for the development and implementation of new frameworks, methodologies and tools. One approach to measure and evaluate the overall corporate sustainability is to use Multi Criteria Decision Making (MCDM) methods. Since there are many complex interdependencies among the used sustainability KPIs and their relations are uncertain (nondeterministic), the Fuzzy Analytic Network Process (FANP) appears to be an appropriate tool for aggregated assessing the sustainability performance. The aim of this paper is to eliminate the defined gap in research and practice by developing and verifying a methodology for aggregated sustainability performance assessment of an industrial corporation using the FANP approach. This aim evokes two research questions, which are investigated in this paper: (1) Is the proposed methodology applicable in industrial corporations? (2) What are the critical points and recommendations for implementation of the proposed methodology in practice? The novelty and uniqueness of the methodology is that: (1) It integrates Triple Bottom Line (TBL) concept, KPIs measurement system, Analytic Network Process (ANP) and a fuzzy technique for sustainability performance assessment of an industrial corporation. Literature review has shown that this combination and especially the FANP approach has not been applied for these purposes so far. (2) It includes a system that enables comprehensive and aggregated assessment of a corporation's sustainability performance. There are several different algorithms how to include fuzzy parameters in ANP. These algorithms are described and critically evaluated. We choose the Logarithmic Fuzzy Preference Programming Methodology (LFPPM) as the most suitable method for the sustainability assessment. The case study from metallurgical industry is used to verify the developed methodology and identify critical points and recommendations for its implementation. Following the introduction, the paper continues with a systematic literature review on sustainability performance assessment in industrial corporations using FANP (Section 2). Next, Section 3 provides a brief description of the methods used in this paper, namely, the ANP method and the LFPPM algorithm are described here. The main section is Section 4, which presents the developed methodology for aggregated sustainability performance assessment of an industrial corporation. Methodology verification is done in Section 5using an explanatory case study from metallurgical environment. The paper ends with summarizing results and discussion of critical points and recommendations for implementation of the methodology in practice (Section 6), and conclusions (Section 7). 2. Sustainability assessment in industrial corporations e state-of-the-art analysis Sustainability is currently considered to be one of the leading value-increasing strategies of industrial corporations (Lo and Sheu, 2007). The sustainability concept was presented in ‘Our Common Future’report by the World Commission on Environment and Development (Brundtland Commission) in 1987 (WCED,1987). This report defined sustainability as ‘the development that meets the needs of the present without compromising the ability of future generations to meet their own needs’and introduced three dimensions of sustainability: economic growth, environmental protection, and social equality. This model was further developed into the TBL concept (Elkington, 1998), which attempts to treat all the three dimensions of sustainability with equal importance and thus could be considered an integrative theory of sustainability (Elkington, 1998). Most definitions of the corporate sustainability are based on the TBL concept. The most respected definition is by Sikdar (2003):‘Sustainability is a wise balance among economic development, environmental stewardship, and social equity’.John and Narayanamurthy (2015) defined the corporate sustainability in a similar way as ‘the complete plan of ethical action for an organization which is attempting to transform itself into sustainable, i.e. to become pro-environmental, pro-social, and traditional proeconomic’. 2.1. Sustainability performance assessment in industrial corporations To implement a sustainable strategy, it is necessary to manage sustainability performance effectively. Nevertheless, integrating sustainability into practice towards corporate sustainability performance still represents a relevant gap in the literature and a huge challenge for firms, to which the present research seeks to contribute (Morioka and de Carvalho, 2016). A sustainability performance measurement and assessment system is one of the basic conditions for the successful sustainability performance management. The measurement of the actual economic, environmental and social performance is an essential starting point to understand what, where and how to improve (Beske-Janssen et al., 2015). Assessing and managing corporate sustainability enable to eliminate and reduce risks, confirm compliance with standards and regulations, signal opportunities and threats, reduce costs, increase efficiency, strengthen competitive advantages, facilitate sustainability reporting, and sharpen operational performance (Qorri et al., 2018). There are many frameworks and tools for the sustainability performance assessment (Ness et al., 2007), but none of them is generally used, and only few of them integrate the TBL concept (Taticchi et al., 2013). Several studies have examined the most commonly used frameworks and tools for sustainability performance assessment. According to Beske-Janssen et al. (2015), the most common frameworks and tools were Environmental Management System, Life Cycle Assessment, Audit, Sustainability Balanced Scorecard, and Key Performance Indicators. The latest study by Qorri et al. (2018) identified as the most used approaches Life Cycle Assessment, Analytical Hierarchy Process, Fuzzy set approach, Balance Scorecard, and Data Envelopment Analysis. Although there are many frameworks and tools for sustainability performance assessment, many authors highlighted the need for further research in the area of the integrated assessment approaches incorporating the TBL concept and new generation of decision-support tools (Beske-Janssen et al., 2015;Morali and Searcy, 2013;Reefke and Sundaram, 2017;Taticchi et al., 2015). Most of the above mentioned frameworks and tools are based on a set of indicators (metrics). Ahi and Searcy (2015) and Tajbakhsh and Hassini (2015) provided in-depth investigations of the sustainability metrics. However, in many corporations the sets of indicators are applied and kept disaggregated, which leads to unsatisfactory, unhandy, and inexpressive results (€ Ozdemir et al., 2011). Due to this deficiency, aggregated sustainability assessment approaches were developed. One of the main approaches is the use of MCDM methods (Ness et al., 2007;€ Ozdemir et al., 2011), which transform multiple indicator values to a single dimension. The application of MCDM methods for the sustainability performance assessment is still increasing (Qorri et al., 2018;Seuring, 2013). The most commonly used MCDM method in this area is the Analytic Hierarchy Process (AHP) developed by Saaty (1980).In P. Wicher et al. / Journal of Cleaner Production 241 (2019) 1181322 their study, Diaz-Balteiro et al. (2017) stated that AHP is the most used method for the sustainability assessment systems (27% of appearances). Saaty (1990) generalized this method for complex problems with a number of interdependencies and developed the ANP method. Although the use of this method for the sustainability performance assessment is more desirable, Diaz-Balteiro et al. (2017) found its use only in 4% of the investigated studies. Relevance of AHP/ANP in this area was also confirmed by Qorri et al. (2018) and Taticchi et al. (2015). Diaz-Balteiro et al. (2017) also identified trend in sustainability performance assessment related to the merging of fuzzy techniques with MCDM. This trend can also be observed in general (Mardani et al., 2015). Qorri et al. (2018) argued that both the number of interactions among indicators and level of uncertainty are high when assessing sustainability performance, and recommended a need to enrich ANP with fuzzy techniques to increase the accuracy of the assessment system. 2.2. Sustainability performance assessment in industrial corporations using FANP We performed a literature review of FANP applications in the sustainability performance assessment based on the conclusions of the previous subsection. Tseng et al. (2009) proposed a FANP framework for determining weights of sustainable production performance indicators. Similarly, Amrina et al. (2016) used FANP for finding criteria weights to evaluate sustainable manufacturing (manufacturing plants) in the cement industry. Nevertheless, the ranking of the plants was carried out using a simple score method. Uygun and Dede (2016) also took advantage of FANP to determine criteria weights, but only for green aspects of corporate sustainability performance. Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS) was recommended to rank the green performance of alternative companies. Bhattacharya et al. (2014) used FANP to determine the weights of measures in proposed Green Balanced Scorecard. The FANP approach has already been used for the sustainability performance assessment, but only to evaluate and select suppliers. Based on the literature review, we identified two basic approaches how to use FANP for supplier sustainability performance assessment. First approach combines FANP to find criteria weights with another fuzzy MCDM method to rank suppliers. The most common combination is FANP/FTOPSIS (Govindan et al., 2013;Büyük€ ozkan and Çifçi, 2012). The second approach is to use FANP both for criteria weighing and for suppliers ranking (Büyük€ ozkan and Çifçi, 2011;Petrudi et al., 2018). The literature review has shown that FANP is most-used in the area of the sustainability performance assessment to determine the weights of indicators (criteria). If FANP is used for evaluation of alternatives, then for suppliers ranking only. No FANP application focused on an aggregated sustainability performance assessment system of an industrial corporation was found. 3. Description of the ANP and FANP methods When dealing with a decision making problem where the ‘best’ option from the set of discrete alternatives should be chosen, some of MCDM methods has to be selected. In the case of the problem solved in this paper, choice of method is natural, because a special structure of relationships among (sub-)criteria and alternatives exists. Two very popular methods considering such structure can be distinguished eAHP and ANP. The former one allows only for linear hierarchy structure, meanwhile the latter one enables decision-maker to involve any relationship in the structure (Saaty, 2005). Because even non-linear links have been identified in the problem, the ANP method will be used further. When the uncertainty involved in the input data of the problem is neglectable, it is possible to use ‘ordinary’algorithms of deterministic methods. However, sometimes it is not possible to omit the fact that some data or relations are inaccurate, e.g., measurements are inaccurate, some data are not available, some inputs might be subjective, etc. Two main possibilities how to involve nondeterminacy exist eeither probability distribution of uncertain variables can be estimated otherwise fuzzy sets can be used. In this paper, the use of probability is not appropriate due to the nature of the problem, thus the fuzzy approach is used. 3.1. Analytic Network Process Due to the fact that the ANP method, established by Saaty (1996), has already been described many times, and to keep the reasonable length of the paper, the ANP algorithm is described very briefly in this subsection. For more details and complete list of formulas, see Saaty (1996). Let us have a problem of decision on kalternatives based on n criteria (nodes) sorted in rclusters. Then, let us assume the network structure, which can be generally displayed in (Fig. 1). First, the local weights, normalised for each cluster, for the goal, and for the set of alternatives, are calculated. Second, the dependencies and loops between the clusters and between the clusters and alternatives are taken into account and the global weights are derived. This is done using the supermatrix W, i.e. the squared matrix of size kþnþ1 (the added 1 represents the goal), including the values of the local weights, see Saaty (1990). This supermatrix Wis normalized so that the sum of each column is equal to 1 (a weighted supermatrix Wis calculated). The normalization is necessary for the computational reasons (to guarantee the convergence of the algorithm) and also for easier interpretation. The last step is to transform Wto the limit (final) supermatrix W ∞ using Eq. (1). W∞¼lim z/∞Wz(1) The final (global) weights can be found in the first column of W ∞ corresponding to the goal. Fig. 1. General network structure. P. Wicher et al. / Journal of Cleaner Production 241 (2019) 118132 3 3.2. Basics of fuzzy sets theory A fuzzy sets theory is a very extensive field of mathematics. For the purpose of this paper, only basic knowledge required to understand the fuzzy extension of ANP method is provided. For the readers who are interested in more details of fuzzy theory used in decision-making, see Ramík and Vlach (2012). First of all, the definition of a fuzzy set and membership function which characterizes fuzzy sets are provided, see Def. 1 and Def. 2 (Ramík and Vlach, 2012). Definition 1. A fuzzy subset of Aof Xis the family of subsets A a ⊆X satisfying A 0 ¼X;A b ⊆A a , and A b ¼∩A a ,c a ; b :0 a < b 1. A fuzzy subset A¼fA a g a 2½0;1 of Xis called a fuzzy set. Definition 2. Let A¼fA a g a 2½0;1 be a fuzzy subset of X. The m A :X/½0;1defined by m AðxÞ¼supf a j a 2½0;1;x2A a g is called the membership function of Aand its value is called the membership degree of xin A. It would be very demanding (and not so much practically useful) to work with general fuzzy sets, therefore, in this paper, we work only with triangular fuzzy numbers (TFN), i.e. fuzzy sets with the membership function expressed by (2). This simplification is used in all the studies on Fuzzy AHP (FAHP) or FANP, which have been discovered by the authors of this paper. A TFN Aða l ;a c ;a r Þgiven by Eq. (2) is displayed in Fig. 2. m A¼ 8 > > > > > > > > > > > > > < > > > > > > > > > > > > > : 0;x<al xal acal;al<xac arx arac;acx<ar 0;x>ar: (2) In order to keep better clarity of written text, all fuzzy parameters will be denoted by tilde in the rest of the paper. 3.3. Fuzzy Analytic Network Process The fact that several different algorithms how to include fuzzy parameters into the MCDM model exist is an usual problem of fuzzy extensions of common deterministic MCDM methods. The same applies to Fuzzy ANP method (FANP). To the best knowledge of the authors, all studies published so far face the fuzziness only during the phase when the local weights are derived from Saaty's matrices, and the global weights are calculated identically with the nonfuzzy (real-valued) approach. That is the reason why studies on FAHP have to be also taken into consideration when choosing the most suitable algorithm for this paper. The existing FAHP/FANP approaches can be sorted into three groups: (1) Methods using defuzzification measures, (2) Methods using a -cuts of fuzzy sets without mathematical programming, and (3) Methods using mathematical programming. The methods from the first group are very easy to use. All fuzzy quantities are defuzzified using a defuzzification measure before the weights are derived and the original Saaty's ANP algorithm can be used to solve the problem. However, the reduction of a fuzzy set to a single real number simplifies the problem, and a decisionmaker looses a part of the information. Yager's index (Bilsel et al., 2006), or center of area (Geldermann et al., 2000) can be mentioned as very popular examples of the defuzzification measures. The second group of methods works with a -cuts of fuzzy sets, but it does not exploit mathematical programming and its algorithms. Csutora and Buckley (2001) have come with the direct fuzzification of the l max method, which can be used to derive the weights within the original deterministic AHP/ANP algorithms. A drawback of this approach is that a decision-maker must either to set an a -degree at which the problem is solved, or the weights can be calculated for all a 2½0;1(resulting in a set of weights). Another example of the method in this group is Synthetic Extended Analysis (SEA), which is based on the possibility measure, see Dargi et al. (2014),Rezaeiniya et al. (2014),Srichetta and Thurachon (2012), or Da gdeviren and Yüksel (2008). But, this method suffers from two main drawbacks. First, it often assigns the weights equal to zero, or one (Dargi et al., 2014). Second, the resulting weights do not represent the relative importance of criteria correctly (Dargi et al., 2014). The first drawback has been solved out by Tang and Lin (2011) and their extended SEA method. However, the second drawback still holds there. The last group of methods uses mathematical programming to derive the weights. The first algorithm, Fuzzy Preference Programming Method (FPPM) has been presented by Mikhailov (2003) and further applied by Kiris¸ (2013),orAlmulhim et al. (2012).An advantage of the FPPM algorithm is that the weights are derived using linear programming, which is easy and fast to use. On the other hand, the optimal solution can be non-unique, and thus hard to apply in practice (Wang and Chin, 2011). This drawback has been eliminated by extensions of the original FPPM algorithm. Dargi et al. (2014) have come with the Linear Goal Programming Priority Method (LGPPM). Unlike the original FPPM, goal programming is used here to derive the final weights. The LGPPM algorithm is not suitable in this paper because it provides the weights expressed with fuzzy numbers. On the one hand, the maximum information is preserved in this way, but, on the other hand, we need to get the real-valued local weights to build the supermatrix and finish the ANP algorithm (see Eq. (1)). Therefore, we select the Logarithmic Fuzzy Preference Programming Method (LFPPM) established by Wang and Chin (2011). In the LFPPM algorithm, the resulting local weights are deterministic and they are derived using quadratic programming. Despite the LFPPM algorithm requires the knowledge of quadratic programming, it is not necessary to set an additional artificial input parameter (like an a -degree), it provides the weights well represents the relative importance of criteria, and it does not use a defuzzification measure resulting in unnecessary loss of information. Therefore, LFPPM is the most suitable method to get the real-valued local weights for the ANP method in this study. 3.3.1. LFPPM algorithm This subsection provides the description how to derive realFig. 2. Triangular fuzzy number and its a -cut at a P. Wicher et al. / Journal of Cleaner Production 241 (2019) 1181324 valued local weights from Saaty's pairwise comparison matrices according to Wang and Chin (2011). Let us have a Saaty's matrix ~ Sof size nnwith TFNs fuzzy coefficients ~ s ij ¼ðs l ij ;s c ij ;s r ij Þand the logarithms of these coefficients are computed. In order to avoid computational difficulties, logarithms of TFNs are approximated as follows: ln~ sijzln sl ij;ln sc ij;ln sr ij Identically to the deterministic model, if the Saaty's matrix is absolutely consistent, s ij ¼ w i w j holds for all elements of the matrix. Thus, a membership function of ln w i w j !belonging to the approximate fuzzy judgement ln~ s ij ¼ðln s l ij ;ln s c ij ;ln s r ij Þ, see Eq. (3). m ln~ s ij ln wi wj!!¼ 8 > > > > > > > > > > > > > < > > > > > > > > > > > > > : ln wi wj!ln sl ij ln sc ij ln sl ij ln wi wj!ln sc ij ln sr ij ln wi wj! ln sr ij ln sc ij ln wi wj!>ln sc ij (3) The aim of the method is to find such real-valued vector of weights wfor which the minimal membership degree for all elements a ¼minf m ln~ s ij ðlnðw i =w j ÞÞfor c~ s ij 2~ S ▽ g(displayed in Eq. (3)) is maximized, see Model 4. max a s:t:¼8 > > < > > : m ln~ s ij lnwiwj a c~ sij2~ S▽ wi0i¼1;2;…;n; a 2½0;1; (4) where ~ S ▽ stands for the set of elements above the main diagonal of the Saaty's matrix ~ S. Model 4 can be transformed into the nonlinear programming Model 5 when Eq. (3) is used, see Wang and Chin (2011). min 1  a s:t: 8 > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > : lnwilnwj a ln sc ij sr ij!ln sl ij;c~ sij2~ S▽; lnwiþlnwj a ln sr ij sc ij!ln sr ij;c~ sij2~ S▽; wi0i¼1;2;…;n: a 2½0;1; (5) As mentioned above, Model 5 is nonlinear, but it can be transformed to the linear form using the substitution x i ¼lnw i for i¼ 1;2;…;n. This simplifying step would not be possible if the usual normalization constraint P n i¼1 w i ¼1 is used. So, in line with Wang and Chin (2011), it is advantageous to normalize the weights after t he optimization is done. If inconsistency of the Saaty's matrix is too great, it may happen that it is not possible to find the weights meeting all the fuzzy judgements within supports of the fuzzy elements of the matrix (i.e. meeting all the constraints of Model 5 for a 2½0;1is impossible). Based on Def. 2, it does not make any sense to obtain a membership degree out of ½0;1. Thus, the artificial deviation variables d ij and h ij are added to the left-hand sides of the constraints of Model 5. In order to keep the new artificial variables as small as possible, they are also added into the objective function (sum of squares to eliminate the sign of values and multiplied by prohibitive constant Msuch as 10 4 ). The modified model is as Model 6. min ð1 a Þ2þM,Xn1 i¼1Xn j¼iþ1 d 2 ij þ h 2 ij s:t: 8 > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > : lnwilnwj a ln sc ij sr ij!þ d ij ln sl ij;c~ sij2~ S▽; lnwiþlnwj a ln sr ij sc ij!þ h ij ln sr ij;c~ sij2~ S▽; wi0;i¼1;2;…;n: a 2½0;1; (6) The last step is the substitution x i ¼lnw i for i¼1;2;…;n.In order to guarantee non-negative value of resulting weights, without loss of generalization new constraint x i 1 for i¼1;2;…; nis added. The final model is Model 7. min ð1 a Þ2þM,Xn1 i¼1Xn j¼iþ1 d 2 ij þ h 2 ij s:t: 8 > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > : xixj a ln sc ij sr ij!þ d ij ln sl ij;for c~ sij2~ S▽; xiþxj a ln sr ij sc ij!þ h ij ln sr ij;for c~ sij2~ S▽; xi0;i¼1;2;…;n a 2½0;1 d ij; h ij;i¼1;2;…;n1j¼iþ1;…;n: (7) Despite the fact that Model 7 is nonlinear (quadratic), the existence of the global optimal solution is guaranteed (the objective function is convex and the set of constraints forms the convex set, thus the model presents the problem of convex programming), see e.g. Taha (2004). Let x  i be the optimal solution of Model 7. Then, the local weights can be derived using Eq. (8). w i¼ex  i Pn i¼1ex  i (8) In the paper of Wang and Chin (2011), proof that the results are identical even when values below the main diagonal of the matrix are put into the model, is provided. P. Wicher et al. / Journal of Cleaner Production 241 (2019) 118132 5 3.3.2. Consistency evaluation When using pairwise comparison matrices for decision-making in practice, some degree of inconsistency in pairwise comparisons is acceptable. Saaty (1990) presented the consistency ratio for realvalued matrices, see Eq. (9), and he proposed the artificial threshold of 0.1 for this ratio as acceptable for a decision-maker. CR ¼ l max n n1,1 RI;(9) where l max is the greatest real eigenvalue of the matrix, nstands for a number of compared elements and RI denotes the random index which is a tabulated variable depending on n, see Saaty (1990). Unfortunately, there is no such clear evaluation of inconsistency for pairwise comparison matrices with fuzzy elements. Let us have a brief look at possibilities how to evaluate the inconsistency here. The first option is to use exactly the same procedure as mentioned above in the deterministic version and make only necessary differences resulting from the fuzziness of the input matrix. Kabir and Hasin (2011) and Sta nkov a and Zapletal (2016) compute the CR using the real-valued matrix of cores of TFNs (i.e. values of fuzzy numbers for which the membership degree is equal to 1), but this simplification causes a piece of information involved in a fuzzy number to be wasted. Gogus and Boucher (1998) presented an extension of the mentioned method ethey proposed to calculate the CR value not only for the cores (CR c ), but also for the real-valued matrices whose elements are calculated as follows (CR g ): s0 ij ¼ffiffiffiffiffiffiffiffiffiffiffi sl ij,sr ij q;for i;j¼1;2;…;n:(10) According to Gogus and Boucher (1998), a fuzzy pairwise comparison matrix is sufficiently consistent if both CR values (CR c ,CR g ) for the corresponding real-valued matrices are less or equal to 0.1. Another option is to use the fuzzy extensions of the real-valued binary operations (Bector and Chandra, 2005) and follow the original algorithm based on Eq. (9) (Rezaeiniya et al., 2014). However, this method requires at least the basic knowledge of fuzzy algebra. Wang and Chin (2011) (the authors of the LFFPM algorithm) have used the value of d (see Eqs. (6) and (7)) to measure the level of (in)consistency (the higher d , the stronger inconsistency among the fuzzy judgements). However, the authors do not mention any threshold analogous to CR ¼0:1. In this paper, we use the approach proposed by Gogus and Boucher (1998) because it is easy to apply even for practitioners (it does not require any deeper mathematical knowledge), it preserves the threshold value from the original Saaty's method, but, on the other hand, it does not ignore the uncertainty hidden in TFNs. In this paper, we use the method of Rezaeiniya et al. (2014) because it works with whole TFNs (not only the cores) and it provides the threshold value. 4. Methodology for aggregated sustainability performance assessment of an industrial corporation The proposed methodology includes the following six phases: (1) KPIs selection and specification, (2) Network structure design, (3) Local weights determination, (4) Global weights determination, (5) Alternatives prioritization, and (6) Results evaluation. The links and steps of each phase are shown in Fig. 3. This scheme includes three feedbacks: (a) From phase 3 to phase 3 eadjusting the pairwise comparisons in case of their inconsistency. (b) From phase 3 to phase 2 eadjusting the non-linear connections. (c) From phase 3 to phase 1 eadjusting a set of selected KPIs and their structure. 4.1. KPIs selection and specification This phase is divided into four steps: (1) KPIs selection, (2) measurement units definition, (3) directions determination, (4) values determination. 4.1.1. KPIs selection The corporation should select a manageable number of the KPIs. For this reason, it is not appropriate to use all KPIs included in corporate sustainability reporting, but only those with the highest priority for the aggregated sustainability performance assessment. For example, the Materiality analysis (GRI, 2018) can be used for this purpose. 4.1.2. Measurement units definition It is necessary to specify a measurement unit for each KPI, which can be relative or absolute. A relative or absolute change is also possible. The proposed methodology makes it possible to use all these methods or their combination. 4.1.3. Directions determination Three possible directions can be distinguished, namely, the greater the better type (‘max’), the smaller the better type (‘min’), and value type if the certain value should be reached (‘value’). 4.1.4. Values determination To obtain the highest possible explanatory power of the aggregated sustainability performance assessment using the selected FANP approach, four kinds of KPIs values should be determined and monitored: (1) Target value ea long-term goal based on the corporate sustainability strategy. (2) Threshold value ea minimum accepted value in the monitored period. (3) Worst value ea longterm worst value based on the corporation historical data. (4) Real value eannual measured values in the monitored period. In general, a longer monitored period means the higher reporting Fig. 3. Scheme of the methodology for aggregated sustainability performance assessment of an industrial corporation. P. Wicher et al. / Journal of Cleaner Production 241 (2019) 1181326 ability of the evaluation obtained. For the KPIs with the ‘value’direction, the threshold and the worst values are defined from both sides, i.e. as deviation from the target value (target value ±deviation). Also the target values of these KPIs should be defined with a certain deviation because managers of industrial corporations do not require absolutely accurate targeting, so it is appropriate to work with a certain tolerance. For calculation purposes, the threshold, worst, and real values of KPIs with ‘value’direction have to be converted to the absolute distance from the target value. In this way the KPIs are converted to the smaller the better (‘min’) type. 4.2. Network structure design We recommend to use the two-level ANP structure to design network for aggregated sustainability performance assessment: (1) main network, (2) sub-networks. 4.2.1. Main network design The main structure contains four clusters: one goal cluster ‘Aggregated Sustainability Performance Assessment’and three criterion clusters, representing three sustainability dimensions (see Fig. 4). The goal cluster includes a single node ‘Goal’. For each criterion cluster, it is necessary to create a set of nodes where each node represents one KPI from the relevant sustainability dimension. Two kinds of connections between the nodes can be defined: linear and non-linear. The linear connections are represented by arrows pointing in one direction away from the goal node to each criterion node/KPI (see full arrows in Fig. 4). These connections express the dependency of the goal on all selected KPIs. While the linear connections are fixed, the non-linear connections need to be defined by managers based on interdependences between individual KPIs. Examples of non-linear connections are shown in Fig. 4 with dashed arrows. The orientation of the arrows determines the direction of dependencies. 4.2.2. Sub-networks design The sub-networks are created for each criterion node/KPI. Each sub-network includes one cluster with a control node (i.e., given KPI) and one alternative cluster (see Fig. 5). The alternative cluster includes alternative nodes for individual KPIs values (target, threshold, and worst value and real values of the monitored period). The sub-network contains only fixed linear connections from the control node to the alternative nodes. 4.3. Local weights determination We recommend to use different methods to determine the local weights for the main network and its sub-networks. 4.3.1. Main network local weights determination Fuzzy pairwise comparison and the LFPPM algorithm are needed to determine the local weights in the main network. Fuzzy cluster and node pairwise comparison matrices are the input for the LFPPM algorithm. To obtain the matrices, the linguistic and numerical characteristics of triangular fuzzy numbers from Table 1 can be used. 4.3.2. Sub-networks local weights determination There is no need to use a fuzzy approach and the pairwise comparison to determine the local weights in the sub-networks because KPI values are precise. For this reason, the local weights are derived from KPI data using normalization. 4.4. Global weights determination It is advisable to determine the global weights for the main network and the sub-networks separately. 4.4.1. Main network global weights determination The global weights of the main network are calculated from the local weights specified in the previous phase using limit supermatrices (see Section 3.1). The resulting weights express an overall significance of the KPIs included. 4.4.2. Sub-networks global weights determination Due to the proposed nature of the sub-networks, the global weights in all the sub-networks are always equal to the local weights specified in the previous phase. 4.5. Alternatives prioritization The use of sub-networks requires synthesizing results for alternatives. There are several ways how to derive the synthesized priority of an alternative. We recommend to use the most natural one, i.e. the additive aggregation, see Eq. (11). Pi¼X m j¼1 SGWij,MGWj(11) where P i is the synthesized priority of the i-th alternative (i¼1;2; …;n, where nis the number of alternatives), SGW ij is the subFig. 4. Main network structure. Fig. 5. Sub-network structure. P. Wicher et al. / Journal of Cleaner Production 241 (2019) 118132 7 network global weight of the i-th alternative and the j-th KPI (j¼ 1;2;…;m, where mis the number of KPIs), MGW j is the main network global weight of the j-th KPI. We recommend to convert the priority values to ‘Idealized values’, which are calculated as the fraction of each alternative priority by the largest priority value, so that the best alternative gets a priority of 1 and the others get their proper proportion less than 1. This conversion allows a better managerial interpretation of the results obtained. 4.6. Results evaluation The phase is divided into two steps: (1) fundamental evaluation, (2) comprehensive assessment. 4.6.1. Fundamental evaluation We propose the following fundamental aggregated sustainability evaluation of industrial corporations based on ‘Idealized values’of the synthesized alternative priorities: (1) basic evaluation, (2) trend evaluation, (3) categorization. The basic evaluation is based on comparison of the aggregated sustainability levels for last year real values, target values and threshold values. The trend evaluation is based on the same logic as the basic evaluation, but it allows to assess the current results in the context of long-term sustainability performance development. The categorization is based on the creation of a number of categories in terms of the performance level of sustainability achieved. The categorization helps to better visualize and simplify the interpretation of the obtained results. We recommend to use the categorization based on the aggregated threshold and target values. A value less than the threshold value means the unacceptable sustainability performance level. On the contrary, a value greater than the target value indicates an excellent sustainability level. We suggest to divide the interval between the target and threshold values into three categories equally (see Table 2). 4.6.2. Comprehensive assessment Based on combining the above evaluation approaches, we developed a system, which provides a comprehensive aggregated sustainability performance assessment (see Fig. 6) and Action matrix, which defines an appropriate corrective actions level to achieve the sustainability performance targets (see Fig. 7). Depending on the trend evaluation and categorization, it is possible to recommend the corrective action level as follows: (1) no actions (NA), (2) small actions (SA), (3) large actions (LA), (4) principal change of strategy (PCS), and (5) total change of strategy (TCS). 5. Case study The explanatory case study from the metallurgical industry was used to verify the developed methodology and to identify critical points and recommendations for its implementation. According to Yin (1984), this type of case study is an appropriate method for this purpose. The subject of the study is a model metallurgical corporation with the performance values based on data from sustainability reports of three metallurgical corporations and World Steel Association (WSA, 2016). The metallurgical industry was chosen as one of the largest industries with high environmental and social impacts and a long-term experience in the sustainability reporting. The corporations’selectionwas based on the list of the top 15 global steelmakers in 2017 (WSA, 2018). We analysed the sustainability reports of all the 15 corporations, and found out that there are three Table 1 Used linguistic and numerical characteristics (Kahraman, 2008). Linguistic variable t-number of preference t-number of non-preference Linguistic variable t-number of preference t-number of non-preference Just equal (1,1,1) (1,1,1) Strong (5,7,9) (1/9,1/7,1/5) Equally important (1,1,3) (1/3,1,1) Very strong (7,7,9) (1/9,1/7,1/7) Weak (1,3,5) (1/5,1/3,1) Extremely strong (9,9,9) (1/9,1/9,1/9) Moderate (3,5,7) (1/7,1/5,1/3) Table 2 Recommended categorization scale (TaV ¼target value, ThV ¼threshold value). Category Interval Excellent >TaV Very good ThV þ2 3ðTaV ThVÞ;TaV½ Good ThV þ1 3ðTaV ThVÞ;ThV þ2 3ðTaV ThVÞ½ Satisfactory ThV;ThV þ1 3ðTaV ThVÞ½ Unacceptable <ThV Fig. 6. Comprehensive aggregated sustainability performance assessment. Fig. 7. Action matrix. P. Wicher et al. / Journal of Cleaner Production 241 (2019) 1181328 steelmakers, which publish its complete set of the sustainability KPIs: ArcelorMittal (2018),POSCO (2018), and Hyundai Steel (2018). The structure of this section follows the six phases of the developed methodology described in Section 4. 5.1. KPIs selection and specification 5.1.1. KPIs selection Based on the comparative study by Lenort et al. (2017), which identified the most important metallurgical KPIs according to GRI topics (GRI, 2018) in three sustainability dimensions (economic, environmental, social), the KPIs for the model metallurgical corporation were selected (see Table 3). 5.1.2. Measurement units definition The units were selected on the basis of the sustainability reports of the three steelmakers (ArcelorMittal, POSCO, Hyundai Steel) and the World Steel Association (see the column ‘Unit’in Table 4). If there were different measurement units in the reports, the mostused unit was selected. 5.1.3. Directions determination The directions of all the KPIs were determined using the expert evaluation of the KPIs character and sustainability aims defined by the analysed steelmakers and World Steel Association, see the column ‘Direction’in Table 4. 5.1.4. Values determination All input values were determined based on the available data of the selected metallurgical corporations and World Steel Association (see Table 4). Due to the data incompleteness (especially the absence of threshold and worst values), all the values were determined by the expert estimation based on the real data from 2014 to 2017. This approach has been chosen because it reflects their real development across the industry. The four-year monitored period was considered long enough to reflect the industry development trends and to verify the proposed methodology. The conversion of the threshold, worst, and real values of KPIs with ‘value’direction to the ‘min’direction is presented in Table 5. These data represent absolute distances from the target value. 5.2. Network structure design We used SuperDecisions software to build the network structure. 5.2.1. Main network design The main network structure, which expresses dependences among the KPIs defined above is shown in Fig. 8. All interdependences of the non-linear connections were based on the expert estimation. Only the main interdependencies were taken into consideration (see Table 6). 5.2.2. Sub-networks design The network structure includes eleven sub-networks, one for each KPI. The alternative clusters contain nodes for the target, threshold, and worst value and the real values from 2014 to 2017. The example for Investments in new processes and R&D (RDI) is shown in Fig. 9. 5.3. Local weights determination 5.3.1. Main network local weights determination All the pairwise comparison matrices were compiled by expert estimation, and are shown in Tables A.1-A.11, see Appendix. In these tables, one can see that the differences in intensity of importance are relatively low. This is caused by the fact that only the most important KPIs were selected. There are no medium or less significant indicators where these differences would be stronger. A similar situation is related to the sustainability dimensions because Table 3 Sustainability KPIs of the model metallurgical corporation. Sustainability dimension GRI topic KPI Code Economic Economic performance Investments in new processes and R&D RDI Economic value distributed EVD Direct economic value generated DEVG Environmental investments EINV Environmental Materials By-product used BPU Energy Energy intensity EINT Water Water intake WI Emissions Greenhouse gas emissions GHGE Social Employment Employee turnover rate ETR Occupational health and safety Lost time injury frequency rate LTIFR Training and education Training time TT Table 4 Input data for the aggregated sustainability performance assessment. KPI Unit Direction Target value Threshold value Worst value 2014 2015 2016 2017 RDI % of revenue value 1:2±0:11:2±0:51:2±0:7 1.1 0.9 1 1 EVD % of revenue value 98±0:198±198±2 97.5 97.6 98 98.5 DEVG % annual change max 10 0 20 111 815 EINV % of revenue value 0:5±0:10:5±0:40:5±0:45 0.15 0.21 0.18 0.17 BPU % max 100 97 95 97.3 98 98.2 98.3 EINT GJ/t steel produced min 20 21 25 21.2 20.8 20.7 20.5 WI m 3 /t steel produced min 2.5 3.5 5 3.6 3.7 3.75 3.7 GHGE t CO 2 steel produced min 1.6 1.8 2 1.88 1.82 1.78 1.75 ETR % min 2 5 10 7.2 3.8 2.7 2.7 LTIFR injuries/million hours worked min 0.5 1 1.5 0.85 0.78 0.76 0.75 TT days/employee value 60±160±10 60±20 50 56 52 51 P. Wicher et al. / Journal of Cleaner Production 241 (2019) 118132 9