Fuzzy ?-topology And A New Fuzzy Covering-based Rough Set Model

In classical rough set theory,the lower(upper)approximation is actually an topological interior(closure)operator.This property of the lower(upper)approximation allows some scholars to study the topological structure of rough sets.Recently,as the generalizations of rough set model,a lot of fuzzy covering-based rough set models are proposed,but the properties of them are barely studied from topological points of view.According to Ma's notion of fuzzy ?-covering,we introduce the concept of fuzzy ?-topology as a tool for the analysis of fuzzy covering-based rough set models.What's more,a new fuzzy covering-based rough set model,of which the fuzzy covering-based lower(upper)approximation is naturally a fuzzy interior(closure)operator under the framework of fuzzy ?-topology,is proposed.Based on the new model,two important conclusions are drawn.One is starting with a random fuzzy set,one can obtain no more than 6 distinct fuzzy sets by applying the fuzzy covering-based lower and upper approximations to it successively.Another one is that given a finite fuzzy ?-covering,there exists an unique irreducible and B-irreducible fuzzy ?-covering which generates the same fuzzy covering-based lower and upper approximations as the former does.