A New Entropy Measure and COPRAS Method for Spherical Fuzzy Sets

Abstract

One of the best ways to handle the ambiguity and unpredictable nature of decision-making is through fuzzy logic, and one of the most recent developments in this area is the concept of spherical fuzzy sets. Since the squared total of membership, non-membership, and hesitation degrees should be between 0 and 1, and each degree should be defined in [0, 1], the hesitation of the decision-maker(s) about an attribute can be conveyed more thoroughly. The ambiguity of a fuzzy set is computed with the help of an entropy measure, and the available entropy measures for spherical fuzzy sets have various limitations. So, in this study, we suggest an innovative entropy measurement for spherical fuzzy sets and demonstrate its capacity to satisfy the axiomatic requirements. We compared the proposed entropy metric and all currently available spherical fuzzy entropy metrics, considering different factors, including attribute weight computation, linguistic hedges, and ambiguity computation. With the help of the proposed entropy metric, we introduce the Complex Proportional Assessment method for spherical fuzzy sets and illustrate it with a numerical example.