Three types of fuzzy covering-based rough set models

In this paper, three new types of fuzzy covering-based rough set models are proposed. First, the membership-degree-based fuzzy covering rough set is defined in the fuzzy covering approximation space by separately comparing the membership degree of each object belonging to the approximated fuzzy set with those of the component fuzzy sets in the fuzzy covering for the same object. Second, the membership-function-based fuzzy covering rough set is obtained by globally comparing the membership function of the approximated fuzzy set with those of the component fuzzy sets in the fuzzy covering. Finally, the membership-function-based fuzzy covering rough set model is generalized to the fuzzy β-covering approximation space. The properties of these new rough set models are discussed. Furthermore, the relationship between these new rough sets and the relationship between the new rough set and Pawlak rough set are described.