Fuzzy Rough Sets Based On Logical Operators

Rough set theory is a mathematical tool of dealing with uncertain information, and Pawlak put forward this theory at 1982. At present, it has developed to be an important research direction of artificial intelligent, it has very extensive latent applying background at the field of Data Mining.Pawlak rough set was established at the base of equivalent relation. For generalizing the application area of rough set theory, Pawlak rough set model is generalized to many models included fuzzy rough set model,probability rough set model,alterable precision rough set model and the rough set model under the generic binary relation etc. In this paper, fuzzy rough sets based on logical operators are researched. Material work is done as follows:Firstly, a general formula norm is given for the approximation operators of fuzzy sets using the triangular norm and its co-nom. And another general formula norm is given using a triangular norm and an implicator. Basic properties of fuzzy rough sets are investigated.Secondly, the connections between fuzzy relations and fuzzy rough approximation operators are examined.Finally, based on closure and interior operators , we discusses the topological structure of fuzzy rough sets. In a approximation space which is based on a reflexive and t-transitive fuzzy relation, it is proved that the upper and lower approximations of fuzzy sets are closure and interior operators of a fuzzy topology respectively.