Abstract
Spherical fuzzy set (SFS) is a modified version of fuzzy set (FS) to cope with uncertainty and complicated data in real-decision theory. In this article, some similarity measures, called cosine similarity measure (CSM), weighted cosine similarity measure (WCSM), set-theoretic similarity measure (STSM), weighted set-theoretic similarity measure (WSTSM), gray similarity measure (GSM), and weighted gray similarity measure (WGSM) are utilized in the setting of SFSs. Further, the information energy, correlation co-efficient (CC) and weighted correlation co-efficient (WCC) of SFSs are also introduced in this manuscript. The established measures based on SFSs are utilized in the setting of pattern recognition and medical diagnosis to express the validity and reliability of the explored measures with the help of some numerical examples. The projected measures based on SFSs are compared with existing measures, to show that the established measures for SFSs are more generalized than existing measures. The advantages and sensitive analysis of the investigated measures are also discussed in detail.
Highlights
To cope with awkward information in decision making, the theory of fuzzy set (FS) was explored by Zadeh [1]
The advantages and sensitive analysis of the investigated measures are discussed in detail
PRELIMINARIE In this study, we review some notions of picture FS (PFS), Spherical fuzzy set (SFS) and their fundamental properties
Summary
To cope with awkward information in decision making, the theory of fuzzy set (FS) was explored by Zadeh [1]. If the sum of truth and falsity grades is greater than 1, the IFS fails For coping with such types of cases, Yager [9] established the notion of Pythagorean FS (PyFS). The human voters divided into three groups like vote for positive, abstinence, negative For coping with such types of cases, picture FS (PFS) was established by Cuong and Kreinovich [25], as more generalized than existing tools. After IFS, the PFS has achieved more attention from researchers and it is utilized extensively in the setting of decision making [26] problems, clustering algorithm [27], [28], and medical diagnosis [29]–[31].
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