Research on Expression of Rough Equality Sets

Rough equality is an important area of rough set theory. The connotation is analyzed in this paper. According to basic concepts of rough set theory, it is proved that different rough sets have the same upper and lower approximations, and the sufficient and necessary condition of rough equality sets is proposed. The properties of rough equality are discussed. This paper focus on that rough equality problem can be solved. Two available methods are presented to describe rough equality set. By improving expression of rough membership function, one way is to change rough membership function of element into rough membership function of equivalence class which is concise. By combining with fuzzy set, the other way is to introduce fuzzy membership function which is valid.