| 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.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. Based on the Fuzzy Rough Set theory ,in fuzzy information processing, based on the features of Vague sets and fuzzy sets,taking voting model as example,methods for transforming Vague sets into fuzzy sets are analyzed to measure Fuzzy information ignorance in this paper. It is found to be a many-to-one mapping relation to transform a vague set into a fuzzy set.Finally, a new transformation method is presented, and its validity is explained by taking examples. Moreover, the application of the new method in Multi criteria Fuzzy Decision Making problems are discussed.Similarity measure of vague set is one of the most important technologies in various applications fields of vague set.Several similarity measures are introduced in the paper, on the basis of which, a new method of similarity measure is introduced in this paper, and proved to satisfy the axiom defined above. Compared with the measures of similarity between Vague sets given by present articles, the method is more differentiated, rational and close to people's understanding. |
PDF Full Text Request