Rough set theory based on two universal sets and its applications

For two universal sets UU and VV, we define the concept of solitary set for any binary relation from UU to VV. Through the solitary sets, we study the further properties that are interesting and valuable in the theory of rough sets. As an application of crisp rough set models in two universal sets, we find solutions of the simultaneous Boolean equations by means of rough set methods. We also study the connection between rough set theory and Dempster–Shafer theory of evidence. In particular, we extend some results to arbitrary binary relations on two universal sets, not just serial binary relations. We consider the similar problems in fuzzy environment and give an example of application of fuzzy rough sets in multiple criteria decision making in the case of clothes.