An extension of rough fuzzy set

In rough fuzzy set, equivalence relation is used for approximating the target concept, which is a fuzzy set. In this paper, we extend the equivalence relation in rough fuzzy set to tolerance relation, and propose an extended model named tolerance rough fuzzy set. Furthermore, the properties of the extended model are investigated, and the proofs of the properties are given in the paper. The advantage of the extended model is that it can directly deal with continuous-valued attributes, and it does not require the process of discretization.

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