Optimistic multigranulation roughness of fuzzy bipolar soft sets by soft binary relations and its applications

Two important mathematical methods for addressing uncertainty in data processing are multigranulation rough set (MGRS) and fuzzy bipolar soft set (FBSS). This paper describes a certain kind of multigranulation rough set in the context of multiple soft binary relations. We first define the multigranulation roughness of fuzzy bipolar soft sets in the two universes. Moreover, a detailed study of structural properties has been conducted in order to explore this concept. The key characteristics of the traditional MGRS model are completely preserved in this new approach. Following that, we suggest two decision-making algorithms with respect to aftersets and foresets of the soft binary relations over dual universes. This approach appears to be better suited and more adaptable than other available methods, making it a favorable option for addressing decision-making problems. Finally, we provide a practical application of the suggested approach to a real-world problem.