A Study Of (I,T) Fuzzy Rough Approximation Operators In Fuzzy Covering Rough Models

In many date mining processes,the neighborhood operators play an important role.As the generalization of equivalence classes which were used in the rough model of Pawlak,it also is a tool to deal with uncertainty cased by indiscernibility and incompleteness.Until up to now,there are few studies about the fuzzy neighborhood operators.In this paper,we make a study of neighborhood operators based on fuzzy covering and the(I,T)fuzzy rough approximation operator.The main content of the paper is stated as follows:To extend the original fuzzy neighborhood,we come up with the concept of the?-fuzzy neighborhood operators,and study the reflexivity,the symmetry and the tran-sitivity of the ?-fuzzy neighborhood operators.Moreover,we prove that the ?-fuzzy neighborhood operators form a lattice structure under the inclusion relation of fuzzy set theory,which provides a pretty basic for the further study of(I,T)fuzzy rough approxi-mation operator.With the fuzzy neighborhood operators,we construct the upper approximation op-erators based on the t-norm T and the lower approximation operators based on the Godel implicator I.We study the properties of the fuzzy lower and upper approximation op-erators,which mainly use the properties of the fuzzy neighborhood to characterize the properties of the(I,T)fuzzy rough approximation operator.In addition,we study the relationships among the(I,T)fuzzy rough approximation operators based on the different?-fuzzy neighborhood.To extend the study of(I,T)fuzzy covering rough set models,we give the relationships between the(I,T)fuzzy rough set model and the fuzzy topology.