Cosine and Cotangent Similarity Measures Based on Choquet Integral for Spherical Fuzzy Sets and Applications to Pattern Recognition

Abstract

The notion of trigonometric similarity measures (SMs) for spherical fuzzy sets has become very important in solving various problems in pattern recognition and medical diagnosis. This study proposes some trigonometric SMs with the help of Choquet integral (CI) for spherical fuzzy sets. The proposed trigonometric SMs clearly satisfy the axiomatic definition of classical SMs. We also perform these SMs in pattern recognition problems to examine a comparative analysis of the proposed trigonometric SMs with some existing SMs. Spearman's rank correlation coefficient is utilized to demonstrate the effectiveness of the proposed SMs.

Interval-valued Pythagorean fuzzy multi-criteria decision-making method based on the set pair analysis theory and Choquet integral

“…Then the C N μ p = a p + b p i + c p j of P given by Eqs. (12)(13)(14) in Definition 12 is a rational CN.…”

“…Proof For an IVPFN P = [a, b], [c, d] , to prove that the CN μ p = a p + b p i + c p j given by Eqs. (12)(13)(14) is a rational CN, we need to prove that 0 ≤ a p ≤ 1, 0 ≤ b p ≤ 1 and 0 ≤ c p ≤ 1. Since a p ≥ 0, c p ≥ 0, then a p + c p ≥ 0.…”

“…Therefore, a concept of Pythagorean fuzzy set (PFS) is introduced by Yager, of which the square sum of membership degree and non-membership degree is less than or equal to one [11]. As extensions of PFS, Smarandache [13] introduced the refined Pythagorean fuzzy sets, Ünver [14] defined Spherical Fuzzy Sets and Zhang [15] proposed a concept of interval-valued Pythagorean fuzzy set (IVPFS). As powerful tools to deal with vagueness and uncertainty involved in MCDM problems, theories and applications of these sets have recently been extensively studied in the literature.…”

Lifetime prolongation of a wireless charging sensor network using a mobile robot via linear Diophantine fuzzy graph environment

“…Graph theory in fuzzy environment is gaining more utilization in designing real-time situations where the quantity of data intrinsic in the structure fluctuates with varying measures of accuracy. Fuzzy models are gaining popularity as they attempt to reduce the disparities among classical digital prototypes used in engineering, technology, and research and symbolic prototypes used in expert systems [23,26,30,33,44,47,53,54].…”

“…Cycles and co-cycles was introduced and investigated by Mordeson and Nair [32]. Sunitha and Vijaykumar [46,47] also introduced the definition of complement of a FG, and also investigated the properties of fuzzy tree, fuzzy bridges, and fuzzy cut vertex and procured several applications in metric spaces.…”