Two Ranking Methods About Fuzzy Number And Its Application

With the development of fuzzy mathematics, a series of fuzzy theories including fuzzy programming and decision-making have been applied to every aspect of life. As an important part of the fuzzy decision and fuzzy programming, fuzzy ranking, in recent years, has been analyzed by an increasing number of scholars who have already put forward plenty of ranking methods. However, due to the semi order characteristic of fuzzy mathematics itself, there is no unified method to rank fuzzy number recently. By summarizing the existing methods of sorting, the starting point which has been proposed is to define ranking indicators on the base of properties of fuzzy membership functions. For example, the earliest Yager’s ranking index, Lea-Li’s ranks fuzzy numbers according to the mean or variance of membership function image and various ranking methods of the centroid. According to the actual production experience, if the practical result of one method can meet public expectation, this method could be analyzed deeply so that it would be applied directly. Thus, as for the fuzzy ranking, because of its uncertainty, further researches should be done to obtain a better method.This paper focuses on the rank of fuzzy numbers and its application mainly from the following aspects:1. After analyzing the existing fuzzy ranking method and compare advantages and disadvantages of them, we find the theoretical foundation for the following new ranking method.2. For fuzzy numbers with the same maximum membership degree, this paper gives a new ranking method by combining concepts of centroid and mean. The fuzzy number ranking method can strictly distinguish the size of the triangle and trapezoid fuzzy numbers which have the same maximum membership degree.3. We propose the concept of the left and right ideal point for the fuzzy numbers appearing different maximum degrees of membership, the fuzzy numbers order can be decided by comparing the distance between the peak point of fuzzy numbers and the left -right ideal point. This method is not only simple in calculation, but also good to solve some fuzzy number ranking problems which are equal in calculation of the original ranking method but visually different.4. Applying the new ranking method of fuzzy number to solve the programming problem with fuzzy coefficients, and proving the accuracy and practicability of this method by analyzing examples.