Similarity measures are extensively used to evaluate the degree of similarity between two distinct entities or collections. Various such measures are discussed in the literature, particularly within the framework of fuzzy set theory. In this study, two types of similarity measures have been proposed under the environment of a T-spherical fuzzy hypersoft sets (TSFHSSs). The TSFHSSs is an extension of the picture fuzzy hypersoft set, representing the intersection of a T-spherical fuzzy set and a fuzzy hypersoft set. This extension allows experts greater flexibility or acceptance in expressing their opinions, without any limitations on components in cases involving sub-parameterizations. The fundamental properties, results of the similarity measures, and theorem on measures have been discussed along with proof. A numerical illustration has been computed for better understanding and reliability of the proposed measures. Additionally, a methodology has been developed based on the introduced similarity measures. Moreover, using a practical instance, the similarity measures for TSFHSSs have been successfully utilized in cluster analysis.

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On Clustering Analysis Under Novel Similarity Measures of T-Spherical Fuzzy Hypersoft Sets

  • Monika,
  • Aman Sharma,
  • Rakesh Kumar Bajaj

摘要

Similarity measures are extensively used to evaluate the degree of similarity between two distinct entities or collections. Various such measures are discussed in the literature, particularly within the framework of fuzzy set theory. In this study, two types of similarity measures have been proposed under the environment of a T-spherical fuzzy hypersoft sets (TSFHSSs). The TSFHSSs is an extension of the picture fuzzy hypersoft set, representing the intersection of a T-spherical fuzzy set and a fuzzy hypersoft set. This extension allows experts greater flexibility or acceptance in expressing their opinions, without any limitations on components in cases involving sub-parameterizations. The fundamental properties, results of the similarity measures, and theorem on measures have been discussed along with proof. A numerical illustration has been computed for better understanding and reliability of the proposed measures. Additionally, a methodology has been developed based on the introduced similarity measures. Moreover, using a practical instance, the similarity measures for TSFHSSs have been successfully utilized in cluster analysis.