A Novel Score Function for Spherical Fuzzy Sets and Its Application to Assignment Problem

In our world today, keeping pace with development of technologies and the expansion of non-absolute data, modelling phenomena becomes very hard and ambiguous, which makes it difficult for deciders to take the optimal decision including the assignment problem, for instance.In this case, leadership is ahead of one serious complex problem, inexact and fuzzy.Spherical fuzzy set (SFS) is disposing the indeterminacy data by the membership, the abstinence and the non-membership functions; it is a generalisation of both Pythagorean fuzzy set (PyFS) and picture fuzzy set (PFS).In this study, some results for SFSs are established first.Then; a novel score function of spherical fuzzy numbers (SFN) is proposed to avoid the comparison problem.In addition; an existing approach to the Pythagorean fuzzy assignment problem is extended to the spherical fuzzy assignment problem (SFAP) with the new proposed score function.Finally, a numerical example and a comparative study are executed to explain the method and validate its advantages.