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.

Evolutionary Search for Stochastic Optimization with Binary Choice Relations Under Fuzzy Modeling

“…They consist of evolutionary algorithms applied to the design of fuzzy systems [9]. Methods for modeling fuzzy systems have received significant development [10,11]. The work of Chen [12] uses a developed modification of a genetic algorithm to optimize the operation of a neural network.…”

“…The use of binary choice relations for decision-making has a history in works from Devraj and Chen [19], Aizerman [20], Aizerman and Litvakov [21], and Sholomov and Yudin [22]. Decision-making in complex systems by selforganization methods developed in the works of Irodov et al [23] and his followers [10]. In the works of Yudin and Sholomov [24] and other authors [25], computational methods of decision theory were considered, in which the problems of finding solutions are formulated in terms of binary relations; thus, the problems of nonlinear mathematical programming are transformed into problems of generalized mathematical programming.…”