Study Of The Relationship Between Vague Set And Rough Set

Cantor developed the concepts of cantor set in 1874. An element is either in a cantor set A, or not in it. There does not exist an element that belongs to A and does not belong to A at the same time. That is, all objects are divided into two classes by cantor set.The objects in real world may not have precisely defined criteria of membership to a concept. The cantor set can not describe information with uncertain borderline. In 1965, Professor Zadeh proposed the theory of fuzzy set. A fuzzy set F is a class of objects U along with a grade of membership function. This membership functionμ_F(U) assigns each object a grade of membership ranging between zero to one. Fuzzy set has been proved to be an excellent mathematical tool for dealing with uncertain and vague objects. It has been used in many uncertain information processing systems successfully, such as fuzzy control, fuzzy expert system, fuzzy decision-making etc. Gau et al developed the concept of vague sets in 1993. Vague set can describe vague information much better than fuzzy set.In this paper, the relationship of Vague set and Fuzzy set is analyzed and the problem of transforming Vague set into Fuzzy set is proposed. It is found to be a many-to-one mapping relation to transform a Vague set into a Fuzzy set. A general model for transforming Vague set into Fuzzy set (GVIF) is developed. The validity of this transforming method is explained by examples. The two transforming methods of Fan Li in [1] are proved to be two special cases of this general transforming model. The application of the GVIF in Multi criteria Fuzzy Decision Making and telecom company NO.10000 problems are discussed.