Information Processing in Project Selection using Fermatean Type Fuzzy Measure

Abstract

The term fuzzy set was coined by Zadeh. Various extensions of fuzzy sets were introduced afterwards allowing diverse applicability. Fermatean fuzzy sets (FFS) serves as an extension of intuitionistic and Pythagorean fuzzy sets. These sets provide a higher expressive capacity to express uncertainty by allowing the sum of cubic powers of membership and non-membership degrees to be at most one.  This work explores a novel Fermatean Fuzzy Divergence Measure (FFDM) based on Neyman and Pearson chi-square measures that preserves essential properties of an information measure. Theoretical properties and some tight bounds are established for proposed FFDM. The practical utility of the measure has been discussed in processing of information for renewable energy selection problem under high uncertainty conditions. The FFDM method is applied to different sets of fermatean fuzzy numbers in order to deduce the maximum correspondence or minimum divergence between the ideal and proposed projects. The most feasible project is then selected based on assigned ranks. The results obtained successfully depict accuracy and reliability of the results. Integration of measure with MCDM uncertainty reduction yields improved decision stability in real world scenarios. The contribution of the proposed FFDM enriches the applicability in complex vague data-based problems where precision under uncertainty seems critical.