On fuzzy rough sets based on tolerance relations

  • Authors:

  • Yao Ouyang;Zhudeng Wang;Hua-peng Zhang

  • Affiliations:

  • Faculty of Science, Huzhou Teacher's College, Huzhou, Zhejiang 313000, People's Republic of China;Department of Mathematics, Yancheng Teachers University, Jiangsu 224501, People's Republic of China;School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210046, People's Republic of China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

Dubois and Prade (1990) [1] introduced the notion of fuzzy rough sets as a fuzzy generalization of rough sets, which was originally proposed by Pawlak (1982) [8]. Later, Radzikowska and Kerre introduced the so-called (I,T)-fuzzy rough sets, where I is an implication and T is a triangular norm. In the present paper, by using a pair of implications (I,J), we define the so-called (I,J)-fuzzy rough sets, which generalize the concept of fuzzy rough sets in the sense of Radzikowska and Kerre, and that of Mi and Zhang. Basic properties of (I,J)-fuzzy rough sets are investigated in detail.