On The Approximations And Reduction In Fuzzy Covering-based Rough Sets

This paper discusses the relationships between a fuzzy approximation space and a fuzzy topology space. The approximations and reduction in fuzzy covering-based rough sets are also studied. Firstly, we discuss the topological characterization in fuzzy approximation spaces. It is proved that a reflexive and transitive fuzzy relation generates a fuzzy topology which produces the same fuzzy approximation spaces. And so is a fuzzy topology space on a universe. Secondly, we discuss the properties of the fuzzy lower and upper approximation operators based on a fuzzy covering of a universe. The reduction of a fuzzy covering is then studied. We also study the axiomatic characterization of the fuzzy lower approximation operator. Thirdly, by making use of the representation theory, we study the fuzzy lower and upper approximation based on a fuzzy covering, the properties of the approximation operators and the reduction of a fuzzy covering of a universe are then examined. The procedure to find a reduction of a fuzzy covering of a universe is also presented. We then get the axiomatic characterizations of the fuzzy lower and upper approximation operator. Finally, we study the problem of knowledge reduction in fuzzy covering-based generalized fuzzy rough sets, and present an algorithm to compute all knowledge reducts by the discernibility matrix.