On fuzzy rough sets based on tolerance relations

Dubois and Prade (1990) introduced the notion of fuzzy rough sets as a fuzzy generalization of rough sets, which was originally proposed by Pawlak (1982) . Later, Radzikowska and Kerre introduced the so-called image-fuzzy rough sets, where I is an implication and T is a triangular norm. In the present paper, by using a pair of implications image, we define the so-called image-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 image-fuzzy rough sets are investigated in detail.