Approaches For The Ranking Of L-R Fuzzy Numbers

In Fuzzy multi-attribute decision, the problem of giving proper order to alternatives finally results in one for giving the ranking relation of L-R fuzzy numbers. In these problems, necessity of procedures to rank L-R fuzzy numbers is obvious. Based on the geometric properties of the curve of L-R fuzzy number's membership, three methods were proposed to ranking L-R fuzzy numbers. The main content of this thesis are as following:1. A L-R fuzzy number is expressed by its membership function, hence the membership function is much more important when ranking fuzzy numbers. Then we may depend on the centroid of membership function which quantity on X-coordinate as the first ranking index. Whereafter a new index is obtained by using the curvilinear centroid of fuzzy number. As the curvilinear centroid of fuzzy number index just only thinks of the central tendency of fuzzy numbers, but regardless of the diffused degree of fuzzy numbers. Then a specification degree index is advanced based on the weighted diffused degree of fuzzy numbers by theα-cuts. Whereafter a new ranking method is obtained by synthesising the two indexes.2. The centroid of fuzzy number's membership, which corresponds to value on the horizontal axis and value on the vertical axis. The Euclidean distance index between the centroid point and original point was proposed. Other wise, a centroid-based area method was proposed, where the fuzzy numbers are compared and ranked in terms of their area distances from their centroid points to the origin.