A novel ranking method for generalized fuzzy numbers based on fuzzy superiority degree

A novel ranking method for generalized fuzzy numbers, based on the fuzzy superiority degree of one fuzzy number over another, is proposed to make pairwise comparisons, and then a ranking strategy based on the proposed method is also developed. The proposed method considers both the elements in the support of each fuzzy number and the corresponding membership values. The merits of the proposed method are to overcome certain shortcomings in ranking methods of the first and the third class, distinguish different types of fuzzy numbers, be consistent with ranking method for interval numbers and have simple calculations to apply in the real life problems. Comparative numerical examples are presented to demonstrate the usage, advantages and applicability of the proposed method. The proposed ranking method can be applied for solving and optimizing engineering problems in fuzzy environment.