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In this manuscript, spherical fuzzy set (SFS) and T-spherical fuzzy set (TSFS) are discussed, which are two generalizations of fuzzy set (FS), intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PFS) and picture fuzzy set (PFS). As TSFS is more capable of processing and expressing unknown information in unknown environment, it is widely used in various areas. However, how to accurately measure the distance between TSFSs is still an unsolved problem. This manuscript discusses some limitations of the existing divergence measures and the problems that the existing divergence measures cannot be applied to the information provided in the TSFSs environment by some numerical examples. Therefore, a new divergence measure under TSFSs structure is proposed by utilizing the advantages of Jensen-Shannon divergence, which is called TSFSJS distance. This TSFSJS distance not only satisfies the distance measurement axiom, but also can better distinguish the difference between TSFSs than other distance measures. More importantly, this TSFSJS distance can avoid counter-intuitive results through the argument of some numerical results in the paper. The proposed approach can deal with more types of uncertain information as demonstrated by establishing a comparative study.

Divergence Measure of T-Spherical Fuzzy Sets and its Applications in Pattern Recognition