Some Results on Specificity of Possibility Distributions

Indian Journal of Advanced Mathematics (IJAM) ISSN: 2582-8932 (Online), Volume-5 Issue-2, October 2025 1 Retrieval Number:100.1/ijam.B120605021025 DOI: 10.54105/ijam.B1206.05021025 Journal Website: www.ijam.latticescipub.com Published By: Lattice Science Publication (LSP) © Copyright: All rights reserved. Abstract: Specificity of a possibility distribution is akin to the entropy of a probability distribution. It serves an essential purpose to zero in on the maximum probability observation. However, when we discuss the existing definition of possibility distribution, it lacks applicability in real-world problems; hence, specificity also becomes an underrated measure for gauging the degree of uncertainty in a possibility distribution. In this paper, we present new findings on the specificity of a possibility distribution, resulting from our research on data-based semantic information analysis in hybrid human-machine systems. In this research, we propose a new frequency-based possibility and probability measure and formalise a new method for fitting restrictions on data or information available in the system. We will demonstrate that the proposed formula is superior to existing specificity measures and discuss various applications of specificity measures in solving problems related to hybrid systems. We shall summarise this paper by providing a real-world application of the proposed measure. Keywords: Possibility Distribution, Restriction, Specificity, Hybrid System, Semantic Information I. INTRODUCTION Specificity is a key concept in possibility distribution theory, much like entropy is in probability distributions. The idea of specificity is deeply rooted in possibility theory. Specificity of a possibility distribution represents the degree to which a possibility distribution points to a single observation. In possibility theory, a possibility distribution (denoted by π) assigns to each possible world or state a degree of possibility ranging from 0 (impossible) to 1 (fully possible). The specificity of a possibility distribution measures how sharply it distinguishes between possible and impossible states—i.e., how "precise" or "informative" it is. A possibility distribution is specific if it rules out as many states as possible, assigning high possibility (close to 1) to a few states and low possibility (close to 0) to the rest. Conversely, a non-specific (or less specific) distribution spreads the possibility more widely, leaving many states as plausible. For example, a possibilility distribution of winning probability {India = 1.0, Australia = 0.5, New Zealand = 0.3, Manuscript received on 16 June 2025 | First Revised Manuscript received on 27 June 2025 | Second Revised Manuscript received on 16 September 2025 | Manuscript Accepted on 15 October 2025 | Manuscript published on 30 October 2025. *Correspondence Author(s) Dr. Jayesh V. Karanjgaonkar*, Assistant Professor, Department of Mathematics, Swami Aatmanand Govt. Eng. Med. Model College, Atari, Raipur (Chhattisgarh). Email: [email protected], ORCID ID: 0009-0000-3894-366X. © The Authors. Published by Lattice Science Publication (LSP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) England = 0.2} is more specific, and {India = 0.8, Australia = 0.8, New Zealand = 0.5, England = 0.5}is less specific. II. SPECIFICITY MEASURES Yager [1] proposed the idea of the specificity of a fuzzy set, which is defined by a function𝑆𝑝:𝑋→[0,1] , having the following properties - 1. ∀𝐴⊂𝑋,𝑆𝑝(𝐴)∈[0,1]. 2. 𝑆𝑝(𝐴)=1⇔𝐴 is a singleton set in 𝑋. 3. 𝑆𝑝(𝜙)=0. 4. For 𝐴,𝐵⊂𝑋, such that 𝐴⊆𝐵𝑆𝑝(𝐴)≥𝑆𝑝(𝐵). 5. Specificity of a set increases if the maximum membership grade increases, and decreases when any other membership grade increases. When 𝑋 is finite, Yager proposed the following formula for the specificity measure 𝑆𝑝(𝐴)=∫ 𝛼  0 1 𝐶𝑎𝑟𝑑(𝐴𝛼)𝑑𝛼 … (1) where, 𝛼=max𝑥∈𝑋𝜇𝐴(𝑥), 𝐴𝛼={𝑥∈𝑋,𝜇𝐴(𝑥)≥𝛼}, and 𝐶𝑎𝑟𝑑(𝐴𝛼) denotes the cardinality of 𝐴𝛼. Yager also defined a new class of specificity measure by the following formula – 𝑆𝑝(𝐴)=𝑤1𝛼1−1 𝑛−1∑ 𝑛 𝑗=2 𝑤𝑗𝛼𝑗 … (2) where 𝛼𝑖 is the decreasing set of possibility grades, with 𝛼1 is the most significant possibility.Also 𝑤𝑗 are weights satisfying the following conditions - 1. 𝑤𝑗∈[0,1] 2. 𝑤1=1 3. 𝑤𝑖≥𝑤𝑗 if 𝑖≤𝑗 4. for all 𝑛≥2, ∑𝑛 𝑗=2 𝑤𝑗≤1 In [2], Dubois and Prade defined the following formulae for the specificity of a normalized fuzzy set 𝐴, provided that all 𝑛 elements of 𝑋 are arranged in decreasing values of 𝜇𝐴 and 𝜇𝐴(𝑥𝑛+1)=0, 𝑆𝑝(𝐴)=∑ 𝑛 𝑖=1 1 𝑖{𝜇𝐴(𝑥𝑖)−𝜇𝐴(𝑥𝑖+1) … (3) Dubois and Prade also proved a one-to-one correspondence between probability and possibility distribution by following a pair of transforms. 𝜋𝑋(𝑥)= ∑ 𝑥′∈𝑋 min(𝑝𝑋(𝑥′),𝑝𝑋(𝑥)) … (4) and its inverse - Some Results on Specificity of Possibility Distributions Jayesh V. Karanjgaonkar Some Results on Specificity of Possibility Distributions 2 Retrieval Number:100.1/ijam.B120605021025 DOI: 10.54105/ijam.B1206.05021025 Journal Website: www.ijam.latticescipub.com Published By: Lattice Science Publication (LSP) © Copyright: All rights reserved. 𝑝𝑋(𝑥𝑖)=∑ 𝑛 𝑗=𝑖 1 𝑗(𝜋𝑋(𝑥𝑗)−𝜋𝑋(𝑥𝑗+1)), for 𝑖=1,2,...𝑛 (5) The specificity of any set 𝐴 of 𝑋 can be seen as the probability of the element which has the most significant membership degree in the above sense of transforms, i.e. 𝑆𝑝(𝐴) is the probability, computed by 𝜋𝑋 using the above equations for the most possible values of 𝑥. However, the above formulations do not support continuous data analysis, as they require arranging the data in decreasing order of membership grades. Hence, we propose a change in the formulae for the specificity measure by removing the precondition of placing the data set. III. RELATING INFORMATION, POSSIBILITY AND SPECIFICITY Possibility conveys two meanings- (i)A physical meaning - Ease to achieve an outcome. and (ii) An epistemic meaning - Logically consistent with available information. Zadeh was the advocate of physical sense, which is reflected in the condition of maximality for the possibility measure 𝑃𝑜𝑠𝑠(𝐴∪𝐵)=max{𝑃𝑜𝑠𝑠(𝐴),𝑃𝑜𝑠𝑠(𝐵)} where 𝐴 and 𝐵 are disjoint sets [3]. The degree of ease of some decision or action which produces the results 𝐴 or 𝐵 is given by the easiest of the two decisions 𝐴 or 𝐵. This idea is reflected in preferences, i.e., when we consider two mutually exclusive alternatives, the one that is most feasible (in any given sense) is usually preferred. The epistemic point of view is practical when incomplete information is present for a decision. Suppose 𝑈 be a set of discourses and 𝑥 be some variable, suppose 𝑥∈𝐸, be the piece of information available, since 𝐸 is a non-empty, non-singleton set, hence it contains more elements and thus 𝐸 has more uncertainty about the actual value of 𝑥, as it can be any value (but only one value) from 𝐸.In this line of thought, we can define a possibility measure by Π𝐸(𝐴)={1if𝐴∪𝐸≠𝜙 0 otherwise i.e. Π𝐸(𝐴)=1 implies that 𝑥∈𝐴 whenever 𝑥∈𝐸 (because 𝐴∪𝐸≠𝜙 ), similarly Π𝐸(𝐴)=0 implies that 𝑥∉𝐴 whenever 𝑥∈𝐸. The following are two scenarios attached to a possibility distribution - A. Complete Knowledge - Suppose 𝐸=𝑢0, for some 𝑢0, then Π𝐸(𝐴)=𝑁𝐸(𝐴)=1,iff𝑢0∈𝐴 i.e., there is one and only one event that is possible and certain. B. Complete Ignorance - If 𝐸=𝑈, then for each 𝐴≠ 𝜙, Π𝐸(𝐴)=1 and for each 𝐴≠𝑈, 𝑁𝐸(𝐴)=0, i.e. everything is possible and nothing is specific. Any kind of data collection for a semantic information-based decision problem has two essential characteristics [4] - 1. Specificity, which provides an interval estimate for the data set. An extensive set is less specific (more uncertain) but better for approximation. 2. Entailment principle, we can always predict a larger set than the actual fuzzy set. If 𝑥∈𝐴 and 𝐴⊂𝐹⊂𝐺, then we can predict the set 𝐺 with more accuracy than set 𝐹. For example, "today is a hot day” can be translated as an interval of values of a variable temperature. The set can be large (less specific), hence there will be a higher chance of representing a hot day. However, as the number of observations increases, more and more frequencies will become equal, and the set will become uniformly distributed, making it impossible to select any particular value. When we reduce the number of observations, the set becomes more specific. Still, there is a chance that the values do not accurately represent the correct temperature to qualify as hot. Thus, a large set is better for prediction; i.e., lowering specificity increases the chance of choosing the proper values of the variable. However, this characteristic works against Maximum specificity, because enlarging the prediction set will reduce the specificity of the estimation. In approximate reasoning with possibilistic distributions, we must work against both of the above theories. We have to predict the correct value with maximum specificity. In statistics, the theory of sampling errors operates on the same basic principle, based on probability distributions. IV. A NEW FORMULATION FOR POSSIBILITY Our work in semantic information analysis for a hybrid man-machine system follows a modified version of Zadeh’s Information Principle [5]. The basic methodology followed in this process is that the data observed by the machine sub-part is converted into a normalised possibility distribution, which is then used in decision-making, prediction, and description of the system. For the analysis of any stream of data, we focus on the mode frequency because it is the most probable and most likely frequency in any sample [6]. Suppose 𝑋={𝑥1,𝑥2,𝑥3...𝑥𝑛} be the set of observations or values of the decision variable. Let 𝐹= {𝑓1,𝑓2,𝑓3...𝑓𝑛} be the respective frequencies. Together 𝑋 and 𝐹 constitutes our version of explanatory database or ED [6]. Suppose that the ED is uni-modular and the mode observation, frequency pair is denoted by (𝑥𝑀,𝑓𝑀). It is also assumed that the mode frequency is much higher than other frequencies. The probability measure, termed natural probability, 𝑃:(𝑋,𝐹)→[0,1] by – 𝑃(𝑥𝑖)=𝑓𝑖 𝑁 (6) Next, we define the possibility measure, termed natural possibility, 𝜋𝑀:(𝑋,𝐹)→[0,1] by – 𝜋𝑀(𝑥𝑖)= 𝑓𝑖 𝑓𝑀 (7) Natural possibility distribution defined by 4.2 converts the ED. (𝑋,𝐹) into a possibility distribution, given the condition of a unique higher mode. We have also defined a probability measure to complement the possibility measure, as well as a proximity value measure. The following table denotes various measures defined to approximate the distribution into an optimal possibility distribution [6]. Indian Journal of Advanced Mathematics (IJAM) ISSN: 2582-8932 (Online), Volume-5 Issue-2, October 2025 3 Retrieval Number:100.1/ijam.B120605021025 DOI: 10.54105/ijam.B1206.05021025 Journal Website: www.ijam.latticescipub.com Published By: Lattice Science Publication (LSP) © Copyright: All rights reserved. Table-I: Various Measures for Possibilistic Analysis, where 𝑵=∑𝒏 𝒊=𝟏 𝒇𝒊 and 𝑵 =𝑵−𝒇𝑴. Measure Formula Natural Probability (P) 𝑃(𝑥𝑖)=𝑓𝑖 𝑁 Natural Possibility(πM) 𝜋𝑀(𝑥𝑖)= 𝑓𝑖 𝑓𝑀 Proximity Value (PV) ∑ 𝑛 𝑖=1 𝜋𝑀(𝑥𝑖)−∑ 𝑛 𝑖=1 𝑃(𝑥𝑖)= 𝑁  𝑓𝑀 Elemental Proximity Value (EPV) 𝜋𝑀(𝑥𝑖)−𝑃(𝑥𝑖)=( 𝑁  𝑁𝑓𝑀)𝑓𝑖 Mode Proximity (MPV) 𝜋𝑀(𝑥𝑀)−𝑃(𝑥𝑀)=𝑁  𝑁 Probability-Possibility Consistency Principle 𝛾= 1 𝑁𝑓𝑀∑ 𝑛 𝑖=1 𝑓𝑖2 Probability to Possibility conversion 𝜋𝑀(𝑥𝑖)= 𝑃(𝑥𝑖) 𝑃(𝑥𝑀) Possibility to Probability conversion 𝑃(𝑥𝑖)= 𝜋𝑀(𝑥𝑖) ∑𝑛 𝑖=1 𝜋𝑀(𝑥𝑖) V. PROPOSING NEW FORMULAE FOR SPECIFICITY We shall use natural possibility and probability as the input in the following formula defined by Yager [1] 𝑆𝑝(𝐴)=𝑤1𝛼1−1 𝑛−1∑𝑛 𝑗=2 𝑤𝑗𝛼𝑗 (8) where 𝑤𝑖∈(0,1) are weights with 𝑤1=1 and decreasing values as 𝑖 increases.The 𝛼1 is the most significant possibility. We replace the respective weights 𝑤𝑖 by probability values 𝑃(𝑥𝑖) and we define 𝛼𝑗=𝜋𝑀(𝑥𝑗), with 𝛼1=𝜋𝑀(𝑥𝑀)=1 (most significant possibility). Using our defined measure of natural possibility, the specificity becomes - 𝑆𝑝(𝑋)=𝑃(𝑥𝑀)𝜋𝑀(𝑥𝑀)− 1 𝑛−1 ∑ 𝑥𝑗≠𝑥𝑀𝑃(𝑥𝑗)𝜋𝑀(𝑥𝑗) =𝑓𝑀 𝑁𝑓𝑀 𝑓𝑀−1 𝑛−1∑𝑓𝑗≠𝑓𝑀𝑓𝑗 𝑁𝑓𝑗 𝑓𝑀 𝑆𝑝(𝑋)=𝑓𝑀 𝑁−1 𝑛−1∑𝑓𝑗≠𝑓𝑀𝑓𝑗2 𝑁𝑓𝑀 (9) (5.2) Above formula defines the specificity of the explanatory database (𝑋,𝐹)through natural possibilities and probability distributions. We have replaced the weights 𝑤𝑖 by the probability of each element 𝑃(𝑥𝑖), save 𝑤1, which is not equal to 1 but takes the value of the mode probability, i.e. 𝑃(𝑥𝑚), so as ∑𝑛 𝑗=2 𝑤𝑗≤1The departure from the formula of specificity defined by Yager is that it can be applied to any frequency-based setting. Here, the maximum specificity will be 1 only when 𝑓𝑀=𝑁, and every other 𝑓𝑗=0 . As the uniformity increases in the sample (non-modal frequencies increase, keeping the sum of frequencies 𝑁 and the number of observations 𝑛 fixed), the specificity decreases. It reaches zero when – 𝑆𝑝(𝑋)=0=𝑓𝑀 𝑁−1 𝑛−1 ∑ 𝑓𝑗≠𝑓𝑀(𝑓𝑗2 𝑁𝑓𝑀) 𝑓𝑀 𝑁=1 𝑛−1 ∑ 𝑓𝑗≠𝑓𝑀 𝑓𝑗2 𝑁𝑓𝑀 =1 𝑛−1[𝑓12 𝑁𝑓𝑚+𝑓22 𝑁𝑓𝑚+... 𝑓𝑛 2 𝑁𝑓𝑚] 𝑓𝑀 𝑁=1 (𝑛−1)𝑁[𝑓12 𝑓𝑚+𝑓22 𝑓𝑚+...𝑓𝑛2 𝑓𝑚] 1= 1 𝑛−1[[𝑓1 𝑓𝑚]2+[𝑓2 𝑓𝑚]2+...[𝑓𝑛 𝑓𝑚]2] 𝑓𝑀 𝑓𝑀=1 𝑛−1[[𝜋𝑀(𝑥1)]2+[𝜋𝑀(𝑥2)]2+...[𝜋𝑀(𝑥𝑛)]2] [𝑓𝑀 𝑓𝑀]2=[𝜋𝑀(𝑥𝑀)]2 =1 𝑛−1[[𝜋𝑀(𝑥1)]2+[𝜋𝑀(𝑥2)]2+...[𝜋𝑀(𝑥𝑛)]2] [𝜋𝑀(𝑥𝑀)]2=1 𝑛−1∑𝑥𝑗≠𝑥𝑀[𝜋𝑀(𝑥𝑗)]2 (10) The above equation provides the limiting values of the sum of squared possibilities, so that the specificity of a member of ED becomes zero. Since [𝜋𝑀(𝑥𝑀)]=1 hence we get ∑𝑥𝑗≠𝑥𝑀[𝜋𝑀(𝑥𝑗)]2=𝑛−1 (11) This provides another condition for zero specificity. Here, the frequency distribution (𝑋,𝐹) is not a uniform distribution, but a non-specific one, i.e., the mode frequency constitutes one portion of the distribution, and the remaining frequencies constitute the reduced portion of the possibility distribution. Recall that the sum of the squared possibilities of a uniform distribution will be 𝑛,, the i.e. number of observations, the above equation provides a condition of zero specificity, by limiting the squared reduced sum to 𝑛−1 Also, since we can put 𝑃(𝑥𝑖)= 𝜋𝑀(𝑥𝑖) ∑𝑛 𝑖=1𝜋𝑀(𝑥𝑖), we get [𝜋𝑀(𝑥𝑀)]2=1 𝑛−1 ∑ 𝑥𝑗≠𝑥𝑀[𝜋𝑀(𝑥𝑗)]2 [𝜋𝑀(𝑥𝑀)]2=1 𝑛−1 ∑ 𝑥𝑗≠𝑥𝑀[𝑓𝑗 𝑓𝑀]2 [𝜋𝑀(𝑥𝑀)]2=1 𝑛−1 ∑ 𝑥𝑗≠𝑥𝑀[𝑓𝑗 𝑓𝑀×𝑁 𝑁]2 [𝜋𝑀(𝑥𝑀)]2=1 𝑛−1(𝑁 𝑓𝑀)2∑ 𝑥𝑗≠𝑥𝑀[𝑓𝑗 𝑁]2 [𝜋𝑀(𝑥𝑀)]2×(𝑓𝑚 𝑁)2=1 𝑛−1 ∑ 𝑥𝑗≠𝑥𝑀[𝑓𝑗 𝑁]2 Putting 𝜋𝑀(𝑥𝑀)=1, 𝑓𝑗 𝑁=𝑃(𝑥𝑗) and𝑓𝑚 𝑁=𝑃(𝑥𝑀) , we get (𝑃(𝑥𝑀))2=1 𝑛−1∑𝑥𝑗≠𝑥𝑀[𝑃(𝑥𝑗)]2 (5.5) which provides an analogous formula for values of probability at zero specificity. In case of a uniform distribution, i.e. 𝜋𝑀(𝑥𝑖)=1 Some Results on Specificity of Possibility Distributions 4 Retrieval Number:100.1/ijam.B120605021025 DOI: 10.54105/ijam.B1206.05021025 Journal Website: www.ijam.latticescipub.com Published By: Lattice Science Publication (LSP) © Copyright: All rights reserved. and 𝑃𝑀(𝑥𝑖)=1 𝑛, using formulae 5, we get - 𝑆𝑝(𝑋)=𝑃(𝑥𝑀)𝜋𝑀(𝑥𝑀)− 1 𝑛−1 ∑ 𝑥𝑗≠𝑥𝑀𝑃(𝑥𝑗)𝜋𝑀(𝑥𝑗) =1 𝑛×1− 1 𝑛−1∑𝑓𝑗≠𝑓𝑀1 𝑛 =1 𝑛−1 𝑛−1×𝑛−1 𝑛 =0 Thus, for a uniform distribution, the above-defined specificity measure 5 becomes zero, i.e., there is no specificity for a uniform distribution. Hence, in our formulation, the specificity of the possibility distribution can be zero when ∑𝑥𝑗≠𝑥𝑀[𝜋𝑀(𝑥𝑗)]2=𝑛−1 or the distribution is uniform. Since the natural possibility distribution is defined based on the unique mode, we shall use the criterion of reduced squared sum in our decision process. VI. EXAMPLE OF TEMPERATURE OF A DAY We have taken a natural language statement Today is a hot day. The resulting possibilistic restriction is (as based on context) temperature (𝑋) is Hot (𝑅), where 𝑋 is a set of real numbers and 𝑅 is a fuzzy set. The membership grades denote the possibility distribution for the day's temperature. We shall convert this problem into a decision problem for a hybrid system. Suppose a machine must decide on an ambient temperature based on natural language statements from human communication. Consider the data shown in the following tableTable-II: Temperature of Month June 2024 Max. Temp. Days Min. Temp. Days 27 1 23 10 28 5 24 6 29 3 25 2 30 3 26 6 31 2 27 5 32 2 28 1 33 3 34 1 35 3 36 1 37 3 38 2 39 1 The above frequency distribution satisfies the requirement of a unique high mode. Hence, using the Natural Possibility Measure, defined by 𝜋𝑀(𝑥𝑖)= 𝑓𝑖 𝑓𝑀 and Natural Probability Measure, defined by 𝑃(𝑥𝑖)=𝑓𝑖 𝑁, we get the following tablesTable-III: Characteristic Calculation Max. Temp. 𝐓 𝐅 𝛑𝐌 𝐏 EPV EPV 27 1 0.2 0.03 0.17 0.17 28 5 1 0.17 0.83 0.83 29 3 0.6 0.1 0.5 0.5 30 3 0.6 0.1 0.5 0.5 31 2 0.4 0.07 0.33 0.33 32 2 0.4 0.07 0.33 0.33 33 3 0.6 0.1 0.5 0.5 34 1 0.2 0.03 0.17 0.17 35 3 0.6 0.1 0.5 0.5 36 1 0.2 0.03 0.17 0.17 37 3 0.6 0.1 0.5 0.5 38 2 0.4 0.07 0.33 0.33 39 1 0.2 0.03 0.17 0.17 Min. Temp. 𝐓 𝐅 𝛑𝐌 𝐏 EPV 23 10 1 0.33 0.67 24 6 0.6 0.20 0.40 25 2 0.2 0.07 0.13 26 6 0.6 0.20 0.40 27 5 0.5 0.17 0.33 28 1 0.1 0.03 0.07 From the above table, the characteristic values of the above distribution are - Table-IV: Characteristics of Distribution Characteristic Max. Temp. Value Min. Temp. Value MPV 0.83 0.67 PV 5.0 2.0 Average TR=34∘C with EPV=0.17 TR=25∘C with EPV=0.13 Specificity 0.1328 0.2653 VII. RESULT In the above example, we have shown a fundamental calculation of instantiation and precisiation of a possibility distribution. It is clear that - • The maximum temperature group has more observation, however they occur in similar frequencies. On the other hand, the minimum temperature group has fewer observations, but they appear at different frequencies. • Similarly, the minimum temperature group is more specific than the maximum temperature group, because the number of distinct observations is less in the minimum temperature group. temperature group, and the mode frequency is higher in mini. temperature group. VIII. CONCLUSION As is clear from the above example, constructing a possibility distribution using context variables and calculating various characteristics is straightforward and can be applied to multiple data settings. Similarly, the calculation of specificity does not require a specific arrangement of frequency or probability distribution; therefore, it can be applied to many more situations involving continuous data streams or fixed datasets. Our formulation of specificity is less restrictive but efficient in the application of various possible scenarios. DECLARATION STATEMENT I must verify the accuracy of the following information as the article's author. ▪ Conflicts of Interest/Competing Interests: Based on my understanding, this article does not have any conflicts of interest. ▪ Funding Support: This article has not been funded by any organizations or agencies. This independence ensures that the research is conducted with objectivity and without any external influence. ▪ Ethical Approval and Consent to Participate: The content of this article does not necessitate ethical approval or consent to participate with supporting documentation. Indian Journal of Advanced Mathematics (IJAM) ISSN: 2582-8932 (Online), Volume-5 Issue-2, October 2025 5 Retrieval Number:100.1/ijam.B120605021025 DOI: 10.54105/ijam.B1206.05021025 Journal Website: www.ijam.latticescipub.com Published By: Lattice Science Publication (LSP) © Copyright: All rights reserved. ▪ Data Access Statement and Material Availability: The adequate resources of this article are publicly accessible. ▪ Author’s Contributions: The authorship of this article is contributed solely. REFERENCES 1. Xu, Z., & Yager, R. R. (2022), A comparative analysis of specificity measures in possibility theory. Information Sciences, 587, 1–18. DOI: https://doi.org/10.1016/j.ins.2022.02.035 2. Dubois, D., & Prade, H. (2016),Measuring specificity in possibility theory. International Journal of Approximate Reasoning, 72, 1–19. DOI: https://doi.org/10.1016/j.ijar.2016.03.006 3. Benferhat, S., & Tabia, K. (2021), Specificity-driven decision making under possibilistic uncertainty. Annals of Mathematics and Artificial Intelligence, 89(3–4), 231–250. DOI: https://doi.org/10.1007/s10472-021-09746-2 4. Destercke, S., & Dubois, D. (2018),On the specificity of a possibility distribution with applications to decision making. Fuzzy Sets and Systems, 336, 95–113. DOI: https://doi.org/10.1016/j.fss.2017.11.003 5. Karanjgaonkar, J., & Jha, P. (2018). Possibilistic analysis of uncertainty and vagueness in semantic communication. International Journal of Research and Analytical Reviews (IJRAR), 5(3), 309-312. DOI: https://doi.org/10.1729/Journal.18405 6. Karanjgaonkar, J., & Jha, P. (2017). On a novel method to measure semantic information through possibilistic restrictions. *IOSR Journal of Mathematics (IOSR-JM), 13*(5), 32-36. DOI: https://doi.org/10.9790/5728-1305033236. AUTHOR’S PROFILE Dr. Jayesh Karanjgaonkar is an Assistant Professor of Mathematics at Swami Atmanand Govt. Eng. Med. Model College, Atari, Raipur (CG). His PHD is in Semantic Information Analysis, which explores the possibilistic analysis of information in a hybrid human–machine system. His research interests include the application of information theory in Management and economic modelling. Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of the Lattice Science Publication (LSP)/ journal and/ or the editor(s). The Lattice Science Publication (LSP)/ journal and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions, or products referred to in the content.