A new exponential knowledge and similarity measure with application in multi-criteria decision-making

The knowledge measure of fuzzy sets (FSs) has drawn greater attention and is still unresolved since it is the complementary idea to fuzzy entropy. The amount of knowledge is important in evaluating fuzzy information. This study proposes an exponential entropy-based knowledge measure for fuzzy sets to quantify the knowledge amount conveyed by fuzzy sets. Intuitive analysis of the characteristics of the knowledge amount in fuzzy sets is introduced, and its value and validity are demonstrated with numerical examples. In addition, a new measures is proposed from the exponential knowledge measure (i.e., exponential similarity measure). These measure are examined for validity, and their characteristics and put forward. Last, a modified Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) strategy based on the suggested similarity measure is suggested to handle a multi-criteria decision-making problem in a fuzzy environment. The effectiveness of the proposed approach is shown By utilizing a numerical example. A comparative analysis is also provided to evaluate the viability of the proposed approach.