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

Abstract

This study aims to develop a new perspective of similarity measures (SMs) for the recently introduced spherical fuzzy sets (SFSs). SFSs have several favorable properties making them superior to other types of fuzzy sets (FSs). As a consequence, SFSs are currently subject to extensive study to establish robust measures. SMs are one of the known measures of FSs. In the spherical fuzzy environment, some of the extant SMs cannot satisfy the axioms of similarity and provide counter-intuitive cases. Moreover, these conventional SMs are generalizations of SMs 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 SM is introduced. While the conventional SMs are based on the position of the SFSs relative to each other, the novel SM is based on the effect of each evaluation on decision-making. First, an extensive review of the SMs for SFSs is presented. Second, the new concept of cognitive impact is introduced in the spherical fuzzy environment. Then, the novel SM is developed. A comparative analysis between the novel SM and the extant SMs is conducted. Finally, a multi-criteria decision-making problem is solved, namely green supplier selection using the proposed cognitive-based SM to check its applicability and its validity.