A Cognitive-Based Similarity Measure for Decision-Making with Spherical Fuzzy Information

Abstract

The study aims to develop a new perspective of similarity measures for the recently introduced spherical fuzzy sets (SFSs). SFSs have several favorable properties making them superior to other types of fuzzy sets. As a consequence, SFSs are currently subject to extensive study to establish robust measures. Similarity measures are one of the known measures of fuzzy sets. In the spherical fuzzy environment, some of the extant similarity measures cannot satisfy the axioms of similarity and provide counter-intuitive cases. Moreover, these conventional similarity measures are generalizations of similarity measures for intuitionistic and Pythagorean fuzzy information. None of them reflects the cognitive dimension of a SFS. Hence, the concept of the cognitive impact of a SFS is introduced. The cognitive impact is the logical implications for what human perception ought to ensue. Based on this concept, a new similarity measure is introduced. While the conventional similarity measures are based on the position of the SFSs relative to each other, the novel similarity measure is based on the effect of each evaluation on decision-making. First, an extensive review of the similarity measures for SFSs is presented. Second, the new concept of cognitive impact is introduced in the spherical fuzzy environment. Then, the novel similarity measure is developed. A comparative analysis between the novel similarity measure and the extant similarity measures is conducted. Finally, a multiple criteria decision-making (MCDM) problem is solved namely, green supplier selection using the proposed cognitive-based similarity measure to check its applicability and its validity.