Defuzzification method for ranking fuzzy numbers based on centroids and maximizing and minimizing set

Abstract

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.

Keywords

• Fuzzy numbers
• Centroids
• Maximizing set
• Minimizing set
• Index of optimism