Novel similarity measures for T-spherical fuzzy sets and their applications in pattern recognition and clustering

Abstract

T-spherical fuzzy sets, the direct extension of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets are examined in this composition, and a mathematical examination among them is set up. A T-spherical fuzzy set can demonstrate phenomenon like choice utilizing four trademark capacities indicating the level of choice of inclusion, restraint, resistance, and exclusion, another example of such situation is that human opinion cannot be restricted to yes or no but it can be yes, abstain, no and refusal. T-spherical fuzzy set can deal the said situation with a boundless space. With the assistance of some mathematical outcomes, it is talked about that current similarity measures have a few drawbacks and could not be implemented where the data is in T-spherical fuzzy mode. Thus, some new similarity measures in T-spherical fuzzy environment are proposed, with the assistance of certain outcomes, it is demonstrated that the suggested similarity measures are generalization of current ones. Further the proposed similarity measures are applied in pattern recognition with numerical supportive examples. The maximum spanning tree clustering algorithm has been extended into T-spherical fuzzy context and supports our theory with numerical examples. A parallel investigation of fresh and existing similarity measures have been made and some of the benefits of designated work have been discussed.

Some T-Spherical Hesitant Fuzzy Shapley Bonferroni Mean Operators and Their Applications

“…Wang and Chen [25] proposed the Tspherical fuzzy ELECTRE method based on the Minkowski distance measures. Saad and Rafiq [26] developed some new T-spherical fuzzy similarity measures and applied them in the clustering algorithm. Yang and Pang [27] developed some T-spherical fuzzy cross-entropy measures and presented the T-Spherical fuzzy ORESTE method.…”

Analysis of T-Spherical Fuzzy Matrix and Their Application in Multiattribute Decision-Making Problems

“…To handle the situation, the concept of T-spherical fuzzy set (TSFS,) which rectifies these limitations, was proposed in [35] having the condition (PD) n + (AD) n + (NPD) n ∈ [0, 1]. Some new similarity measures for TSFSs have been developed by Ullah et al [36] and Saad and Rafiq [37]. e divergence measure of TSFSs with their applications in pattern recognition has been discussed in [38].…”

Correlation coefficients for T-spherical fuzzy sets and their applications in pattern analysis and multi-attribute decision-making

“…Further, in generalization of FSs, IFSs, PyFSs, PFSs, and SFSs, a novel and most helpful tool in fuzziness was proposed by Mahmood et al ( 2018 ) known as TSFS, which has no limitations at all. For some applicable work in this direction, we may refer to Ullah ( 2018 , 2020 ), Wu ( 2020 ), Garg ( 2018 ), Munir ( 2020 ), Saad ( 2022 ), and Akram ( 2022 ).…”