Distance measures of r,s,t-spherical fuzzy sets and their applications in MCGDM based on TOPSIS

The T-spherical fuzzy set is a useful generalization of other fuzzy structures such as fuzzy, intuitionistic fuzzy, Pythagorean fuzzy, picture fuzzy, q-rung orthopair fuzzy, and spherical fuzzy sets. The notion of r,s,t-spherical fuzzy set was defined by the researchers as a generalization of T-spherical fuzzy sets. In this paper, the set operations of r,s,t-spherical fuzzy sets are defined and the arithmetic operations between the r,s,t-spherical fuzzy numbers are redefined, and some results related to defined operations are derived. Also, distance measures between two r,s,t-spherical fuzzy sets based on Hamming, Hausdorff, and Euclidean distance measures are introduced. Furthermore, a multi-criteria group decision-making (MCGDM) method is developed based on the TOPSIS method by using the proposed distance measure. Finally, to show the process of the proposed MCGDM method, a numerical example is given.