Similarity Measures for T-Spherical Fuzzy Sets with Applications in Pattern Recognition

Abstract

In this manuscript, two generalizations of fuzzy sets, intuitionistic fuzzy sets and picture fuzzy sets, known as spherical fuzzy sets and T-spherical fuzzy sets, are discussed and a numerical and geometrical comparison among them is established. A T-spherical fuzzy set can model phenomena like voting using four characteristic functions denoting the degree of vote in favor, abstinence, vote in opposition, and refusal with an infinite domain, whereas an intuitionistic fuzzy set can model only phenomena of yes or no types. First, in this manuscript, some similarity measures in the frameworks of intuitionistic fuzzy sets and picture fuzzy sets are discussed. With the help of some numerical results, it is discussed that existing similarity measures have some limitations and could not be applied to problems where information is provided in T-spherical fuzzy environment. Therefore, some new similarity measures in the framework of spherical fuzzy sets and T-spherical fuzzy sets are proposed including cosine similarity measures, grey similarity measures, and set theoretic similarity measures. With the help of some results, it was proved that the proposed similarity measures are a generalization of existing similarity measures. The newly-defined similarity measures were subjected to a well-known problem of building material recognition and the results are discussed. A comparative study of new and existing similarity measures was established and some advantages of the proposed work are discussed.

On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition

“…These similarity measures are utilized in MADM problems. Ullah et al [40] developed few similarity measures for T-spherical fuzzy set and utilized those similarity measures in building material recognition problems. [41][42][43] discussed some MADM problems in bipolar-valued hesitant fuzzy environments, while [44,45] are based on some medical diagnosis and MADM problems based on Tspherical fuzzy and linguistic cubic fuzzy information.…”

Algorithm for T-Spherical Fuzzy Multi-Attribute Decision Making Based on Improved Interactive Aggregation Operators

“…For this environment, Mahmood et al [34] presented some aggregation operators for T-SFSs. Later on, Ullah et al [35] presented the concept of the symmetry measures for handling the uncertainties under the T-SFSs environment, and applied it to solve the decision-making problems. However, from the existing work, it is noticeable that the existing AOs under the IFSs, PFSs, etc., have failed to handle the situations under some certain cases.…”

Evaluation of Investment Policy Based on Multi-Attribute Decision-Making Using Interval Valued T-Spherical Fuzzy Aggregation Operators

“…Furthermore, as discussed in the first section, there are some situations, such as voting or decision-making, where opinions may involve more than two or three aspects. To deal with such situations, the TSFS has been proven to be useful [22,23,62]. Therefore, the idea of TSFSs is further strengthened by the introduction of the IVTSFS.…”

“…Due to the larger variety of characteristic functions with no limitation, several much-needed ideas can be developed in the framework of TSFSs, such as the aggregation theory of TSFSs, graphs of TSFSs, and similarity and distance measures of TSFSs. Some work on the aggregation of TSFSs, relations of TSFSs, and similarity measures of TSFSs is abound [22,23].…”