A multigranulation rough set over two universes delivers a unique perspective on the combination of multigranulation information. This paper presents the pessimistic multignualtion rough set over dual universes based on soft binary relations. Firstly, a new pessimistic multigranualtion rough set over dual universes based on two soft binary relations has been developed, and their properties are derived. Then we extend this idea and present pessimistic multigranulation roughness over dual universes based on the finite number of soft binary relations. Finally, we present an example to illustrate our proposed multigranualtion rough set model.

A fascinating extension of Pawlak rough set theory to handle uncertainty is multigranulation roughness, which has been researched by several researchers over dual universes. In light of this, we proposed a novel optimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes and established two types of approximations of a fuzzy set with respect to forsets and aftersets of the finite number of soft binary relations in this article. We obtain two sets of fuzzy soft sets in this way, referred to as the lower approximation and upper approximation with respect to the aftersets and the foresets, respectively. Next, we look into some of the lower and higher approximations of the newly multigranulation rough set model's algebraic properties. Both the roughness and accuracy measurements were defined. In order to show our suggested model, we first develop a decision-making algorithm. Then, we give an example from a variety of applications.