Tolerance Rough Fuzzy Set Model

In rough fuzzy set model, the approached target concept is a fuzzy set, the knowledge used for approaching the target concept is equivalence relation, in other words, the attributes used for representing the object is of discrete value. However, in many practical applications, the attributes used for representing the object is of real value. A rough fuzzy set model named tolerance rough fuzzy set which can deal with data sets with real-valued attributes is investigated in this paper, the main works include:(1) The equivalence relation in rough fuzzy set model is extended to tolerance relation, and the tolerance rough fuzzy set model is proposed.(2) The properties of the proposed model are studied, the proofs of some properties are given.(3) The quantitative characteristics of the proposed model are discussed, an attribute reduction algorithm based on significance is presented. In addition, the relationships between the proposed model and other related models are also discussed, when the tolerance relation is degenerated into equivalence relation, the tolerance rough fuzzy set model becomes the rough fuzzy set model. Tolerance rough fuzzy set model extends the application of rough fuzzy set.