The Performance Order of Fuzzy Numbers Based on Bi-Symmetrical Weighted Distance

In this paper, a new approach is prposed for ordering fuzzy numbers based on bi-symmetrical weighted distance. The proposed method considers the bi-symmetrical weighted function and the bi- symmetrical weighted distance of fuzzy numbers to rank fuzzy numbers. Some examples to compare the advantage of this approch with the existing metric index ranking methods is illustrated. The process to rank the fuzzy numbers of this method is easier than that of other efforts. This method can effectively rank various fuzzy numbers and their images and overcome the shortcomings of the previous techniques. AA  ; if R(A i) = R(A j), then Ai~A j; if R(A i)>R(A j), then ij AA  . Moreover, the distance method contradicts the CV index in ranking some fuzzy numbers. Consider the three fuzzy numbers, A = (0.2,0.3,0.5), B = (0.17,0.32,0.58) and C = (0.25,0.4,0.7) utilized in Cheng (9). In his distance method, R(A) = 0.59, R(B) = 0.60 and R(C) = 0.66, resulting in the ranking order ABC  . From this result, the researchers can logically infer the ranking order of the images of these fuzzy numbers as A B C −−−   . However, in the distance method, the

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