Multi-criteria decision-making based on intuitionistic fuzzy exponential knowledge and similarity measure and improved VIKOR method

Atanassov intuitionistic fuzzy sets (AIFSs) are substantially more effective at capturing and processing uncertainty than fuzzy sets. More focus has been placed on the knowledge measure or uncertainty measure for building intuitionistic fuzzy sets. One such use is to solve multi-criteria decision-making issues. On the other hand, the entropy of intuitionistic fuzzy sets is used to measure a lot of uncertainty measures. Researchers have suggested many knowledge measures to assess the difference between intuitionistic fuzzy sets, but several of them produce contradictory results in practice and violate the fundamental axioms of knowledge measure. In this research, we not only develop a new AIF-exponential knowledge measure (AEKM) but also broaden the axiomatic description of the knowledge measure (KM) of the intuitionistic fuzzy set. Its usefulness and validity are evaluated using numerical examples. Additionally, the following four measures result from the suggested AIF-exponential knowledge measure (AEKM) are the AIF-exponential accuracy measure (AEAM), information measure (IM), similarity measure (SM), and dissimilarity measure (DSM). The validity of each of these measures is examined, and their characteristics are explained. The suggested accuracy measure is applied in the context of pattern recognition. To resolve a multi-criteria decision-making (MCDM) dilemma in an intuitionistic fuzzy environment, a modified Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) strategy based on the suggested similarity measure is provided. Choosing a suitable adsorbent for removing hexavalent chromium from wastewater is done using the described methodology.