The Research Of Fuzzy Number Ranking And Similarity Measures Between Vague Sets

There are only two kinds of relations between the elements of the cantor set and the cantor set,including belonging or not belonging to.But when the concept of the set itself is vague, elements cannot be simply regarded as belonging to or not belonging to the set.Thus,the United States of American Cybernetics Professor L.A.Zadeh popularized the concept of cantor set and put forward fuzzy set theory in1965.Because vague set can only express the support and against information,cannot express hesitation.In order to solve the expression to the fuzzy information,Gau and Buehrer put forward another concept dealing with fuzzy information——Vague set theory in the1993.The vague set popularizes the fuzzy set. This article has researched the relevant theoretical knowledge of the fuzzy set and vague set, and mainly done some research work as follows:1. The ranking method of fuzzy number is studied. At present,many scholars have discussed the ranking method about fuzzy number.In this paper,several of the commonly used methods of ranking fuzzy number are analyzed, and are founded that the differential capacity of these methods about the fuzzy number ranking is not good.Therefore,this paper gives the three impacting factors about the fuzzy number size which include weight area of the fuzzy number,the distance between fuzzy numbers and the average fuzzy numbers,fuzzy numbers center point.A new method for fuzzy numbers ranking is put forward according to these three factors.2. The similarity of the vague set is studied.The differential capacity of existing methods about vague set similarity is not good.Therefore, several kinds of vague set similarity measure methods are analysed in this article.Based on their advantages,this paper puts forward a new vague similarity measure and overcomes shortcomings of the existing methods.This method can greatly distinguish the similarity about the vague sets.3. As a result of theoretical knowledge of the vague set is not very mature, coupled with its membership degree for interval value, the data of the vague set is difficult to handle.Many scholars have transformed vague set into fuzzy sets, and use the mature theory knowledge of the fuzzy sets to handle the information of the vague set.This paper analyses the method of existing vague set into fuzzy set, combining with the requirements of the standards about vague set into fuzzy set,so a new method about vague set into fuzzy set is proposed.