Rough set theory for the interval-valued fuzzy information systems

  • Authors:

  • Zengtai Gong;Bingzhen Sun;Degang Chen

  • Affiliations:

  • College of Mathematics and Information Science, Northwest Normal University, Lanzhou 730070, PR China;School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, PR China;Department of Mathematics and Physics, North China Electric Power University (Beijing), Beijing 102206, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2008

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Abstract

The notion of a rough set was originally proposed by Pawlak [Z. Pawlak, Rough sets, International Journal of Computer and Information Sciences 11 (5) (1982) 341-356]. Later on, Dubois and Prade [D. Dubois, H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of General System 17 (2-3) (1990) 191-209] 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.