Optimistic Multigranulation Roughness of Spherical Fuzzy Set Based on Soft Binary Relations and Its Applications to Multicriteria Decision‐Making Problems

A multigranulation roughness over dual universes establishes a unique viewpoint on the mixture of multigranulation data. Spherical fuzzy set is an extension of all existing theories such as fuzzy set, pythagorean fuzzy set, intuitionistic fuzzy set, and picture fuzzy set. This theory gives a more flexible structure for handling uncertainty and inaccuracy in decision‐making problems compared to all the extensions of fuzzy set. This paper introduces optimistic multigranulation roughness of a spherical fuzzy set based on two soft binary relations over dual universes. In this regard, we obtain two spherical fuzzy soft sets with respect to foresets and aftersets. A comprehensive study of the basic properties of this new approach has been studied in order to explore this concept. Then, by extending this idea, we present optimistic multigranulation roughness of a spherical fuzzy set over dual universes based on multiple soft binary relations. Moreover, a decision‐making algorithm depending on these approximations of spherical fuzzy sets is presented, and a practical example to choose a university professor is given. Two different panels of interviewers analyze the candidates based on different parameters by using the spherical fuzzy concept. This approach will be better and more flexible than other existing techniques.