This paper proposes a new method on ranking fuzzy numbers through the process of defuzzification by using maximizing and minimizing set on the triangular fuzzy numbers formed from generalized trapezoidal fuzzy numbers. In this method, a total utility value of each fuzzy number is defined by considering two left and two right utility values along with decision maker's optimism which serves as a criterion for ranking fuzzy numbers and overcomes the limitations of Chen's (1985) [Chen, S. H. (1985). Ranking fuzzy numbers with maximizing set and minimizing set. Fuzzy sets and systems, 17(2), 113-129] ranking method. .

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This paper proposes a new method to rank the parametric form of fuzzy numbers based on defuzzification. The defuzzification process use centroids, value, ambiguity and decision levels on fuzzy number developed from the parametric form of a generalized fuzzy number. The proposed method avoids reducing function to remove lower alpha levels and can overcome the shortcomings in some of the existing fuzzy ranking methods. The proposed method can effectively rank symmetric fuzzy numbers with the same core and different heights, fuzzy numbers with the same support and different cores, crisp numbers, crisp numbers having the same support and different heights, and fuzzy numbers having compensation of areas. A demonstration of the proposed method through examples and a comparative study with other methods in the literature shows that the proposed method gives effective results.

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