Rough Set Theory On The Interval-Valued Fuzzy Information Systems

This paper deal with an interval-valued fuzzy information systems by means of integrating the classical Pawlak.Z rough sets theory with the interval-valued fuzzy set theory, and discuss the basic rough sets theory on the interval-valued fuzzy information systems. In this paper we first define the rough approximation of an interval-valued fuzzy set on the universe U in the classical pawlak.Z approximation space and the generalized approximation space respectively, i.e., the interval-valued rough fuzzy sets model is built. Meanwhile, the basic properties and their interrelations of the interval-valued rough fuzzy sets model in the classical pawlak.Z approximation space and the generalized approximation space are investigated. And then propose an interval-valued fuzzy information systems based on the definition of a binary interval-valued fuzzy relations R∈F⁽ⁱ⁾(U×U) on the universe U, and the rough approximation of a crisp set and an interval-valued fuzzy set of the universe U in the interval-valued information systems (U, R) is given, i.e., the interval-valued fuzzy rough set model is made up, furthermore, the interrelations between these operators and the other rough approximation operators is deliberated. Several interesting properties of the approximation operators which defined in this paper are examined. In addition, the present work discusses the attribute reduction and the knowledge discovery of the interval-valued fuzzy objection information systems and the interval-valued fuzzy equalized-objection information systems respectively, and the knowledge reduction theorems of the interval-valued fuzzy objection information systems is built. Finally, the method and the steps of the knowledge discovery on the interval-valued fuzzy equalized-objection information systems is presented with an practical example.