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On fuzzy rough sets based on tolerance relations |
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| Authors: | Yao Ouyang Zhudeng Wang |
| Affiliation: | a Faculty of Science, Huzhou Teacher’s College, Huzhou, Zhejiang 313000, People’s Republic of China b Department of Mathematics, Yancheng Teachers University, Jiangsu 224501, People’s Republic of China c School of Science, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu 210046, People’s Republic of China |
| 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. |
| Keywords: | Rough sets Fuzzy rough sets Fuzzy implication Involutive Tolerance relation |
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