A novel multigranulation roughness of bipolar fuzzy set over dual universes and its applications

Abstract

In the world, multigranulation rough sets and bipolar fuzzy sets are the practical tools for dealing with the uncertainty, vagueness, and imperfection that frequently arise in decision making problems. The goal of multigranulation rough sets is to characterize uncertain situations in various granularity spaces, whereas bipolar fuzzy sets (BFSs) have the capacity to handle uncertainty as well as informational bipolarity in a variety of contexts. This article examines the optimistic multigranulation rough approximation of a BFS in the light of multi-soft binary relations across two different universes. We investigate some algebraic properties of our newly constructed optimistic multigranulation rough set scheme. Measures of accuracy and roughness are also covered in this paper. Finally, two decision algorithms are designed with respect to aftersets and foresets that are applied to a decision making problem in disease diagnoses, and the applicability of the method is illustrated by a numerical example.