Similarity Measure Of Vague Sets

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 functionμF(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.The similarity measure of two uncertain patterns is important for intelligent reasoning. It is also a key problem to measure the similarity of vague values or vague sets in vague information processing systems. Many methods for similarity measure of vague sets have been proposed in recent years. However, these methods could not precisely describe the essences of the similarity between two vague sets. In this paper, some evaluation criterions for similarity measure of vague set is proposed by analyzing existed similarity measure methods and evaluation criterion. For measuring the similarity of vague sets, a new method is proposed. A new concept named differentiation ability is also developed. Simulation results show that our methods are better than existed methods.