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Rough set theory for the interval-valued fuzzy information systems. (English) Zbl 1138.68564
Summary: The notion of a rough set was originally proposed by Z. Pawlak [Int. J. Comput. Inf. Sci. 11, 341–356 (1982; Zbl 0501.68053)]. Later on, D. Dubois and H. Prade [Int. J. Gen. Syst. 17, 191–209 (1990; Zbl 0715.04006)] introduced rough fuzzy sets and fuzzy rough sets as a generalization of rough sets. This paper deals with an interval-valued fuzzy information system by means of integrating the classical Pawlak rough set theory with the interval-valued fuzzy set theory and discusses the basic rough set theory for the interval-valued fuzzy information systems. In this paper we firstly define the rough approximation of an interval-valued fuzzy set on the universe $$U$$ in the classical Pawlak approximation space and the generalized approximation space respectively, i.e., the space on which the interval-valued rough fuzzy set model is built. Secondly several interesting properties of the approximation operators are examined, and the interrelationships of the interval-valued rough fuzzy set models in the classical Pawlak approximation space and the generalized approximation space are investigated. Thirdly we discuss the attribute reduction of the interval-valued fuzzy information systems. Finally, the methods of the knowledge discovery for the interval-valued fuzzy information systems are presented with an example.

##### MSC:
 68T30 Knowledge representation 68T37 Reasoning under uncertainty in the context of artificial intelligence 68U35 Computing methodologies for information systems (hypertext navigation, interfaces, decision support, etc.)
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