Algebraic Properties of Rough Set on Two Universal Sets based on Multigranulation

The rough set philosophy is based on the concept that there is some information associated with each object of the universe. The set of all objects of the universe under consideration for particular discussion is considered as a universal set. So, there is a need to classify objects of the universe based on the indiscernibility relation (equivalence relation) among them. In the view of granular computing, rough set model is researched by single granulation. The granulation in general is carried out based on the equivalence relation defined over a universal set. It has been extended to multi-granular rough set model in which the set approximations are defined by using multiple equivalence relations on the universe simultaneously. But, in many real life scenarios, an information system establishes the relation with different universes. This gave the extension of multi-granulation rough set on single universal set to multi-granulation rough set on two universal sets. In this paper, we define multi-granulation rough set for two universal sets U and V. We study the algebraic properties that are interesting in the theory of multi-granular rough sets. This helps in describing and solving real life problems more accurately.