A model of granular computing based on rough set theory

Ever since the introduction of the term of granular computing, we have witnessed a rapid development in the topic. Many models and methods of granular computing have been studied. In this paper, we propose a model of granular computing based on rough set theory. The standard rough set theory uses equivalence classes as granules to describe concepts. The partition induced by an equivalence relation forms a granulated view of the universe. Rough membership functions provide us with another view for interpreting rough set. By extending rough membership functions, this paper first examines a granulated view induced by a covering of the universe and defines the operations on the granules, then explores the connections of different levels in the granular structure induced by a partial order sequence of coverings. We indicate that many other granular structures are special cases of what we present here.