A method for ranking fuzzy numbers and its application to decision-making

Since fuzzy numbers represent uncertain numeric values, it is difficult to rank them according to their magnitude. In the paper, a method for ranking fuzzy numbers is proposed. The method considers the overall possibility distributions of fuzzy numbers in their evaluations for ranking and provides users with a method of changing viewpoints for evaluations. Users represent their viewpoints with fuzzy sets. The method evaluates fuzzy numbers with a satisfaction function and the viewpoint given by users and then ranks the numbers according to their evaluation values. The satisfaction function is a measure of comparisons between fuzzy numbers. In order to illustrate the ranking method, two numeric examples are shown, and for the comparative study, our method is compared with four existing ranking methods through eight examples. As an example of potential applications, the proposed method is applied to a decision-making problem: a two-person game with fuzzy profit and loss. The ranking method is used to analyze player choices.