Multi-criteria decision-making based on novel fuzzy generalized divergence and knowledge measures

In a number of fuzzy systems, knowledge measures have been extensively investigated. However, no research on knowledge measures derived from divergence for standard fuzzy sets has been done. This study develops and validates a new generalized divergence measure for fuzzy sets based on the mathematical structure of Csiszár’s divergence. Some of its specific cases, mathematical properties, and performance comparisons are discussed. In addition, exploiting Csiszár’s divergence idea, a class of fuzzy knowledge measures has been established. The proposed fuzzy generalized divergence is then used to derive a new fuzzy generalized knowledge measure. Its efficacy in capturing the amount of useful information in fuzzy sets was demonstrated by comparing it to some strategic information measures. In uncertain multi-criteria decision-making (MCDM) situations, fuzzy entropy is typically adopted to compute the objective weights of criteria. However, it frequently provides unsatisfactory results. New optimization models for generating the objective weights based on the two proposed measures are implemented. These models incorporate both the principles of maximizing deviation and knowledge measures. This research also presents a novel approach based on a single ideal point for integrating Gray Relational Analysis (GRA) with VIKOR (Vlsekriterijumska Optimizacija I KOmpromisno Resenje). The developed technique focuses on discovering the most advantageous alternative, whose performance meets almost every benefit criterion, as well as identifying the criteria that make an alternative less effective. The consistency and rationality of the proposed approach are demonstrated through a numerical illustration along with sensitivity and comparative analysis.