On ∆ Operation over Fermatean Fuzzy Sets: An Application to a De-i-fuzzification Technique

Abstract

Fermatean fuzzy sets, a recent and advanced extension of intuitionistic fuzzy theory, expand the frontiers of uncertainty modeling by incorporating the condition that the cubic-sum of membership and non-membership degrees is bounded by one. This paper introduces the D operation, a novel algebraic construct tailored for Fermatean fuzzy sets, to facilitate richer comparative and transformational relationships between fuzzy evaluations. We rigorously define the D operation and derive several fundamental properties, including its interplay with implication and other fuzzy operations. Furthermore, we propose a specialized de-i-fuzzification method designed for the Fermatean fuzzy framework, enabling crisp representation and interpretation of fuzzy information. A key innovation of this study is the demonstrated synergy between the D operation and de-i-fuzzification, which permits the quantitative rectification of expert evaluation errors.