A Method for Ranking Fuzzy Numbers and Its Application to Game with Fuzzy Profit

Abstract

In this paper, a new method for ranking fuzzy numbers is proposed. Based on decomposition theorem of fuzzy set, firstly, the method considers interval numbers, the relation between lines and interval numbers is discussed in Cartesian coordinates, the distance of dot A to lines l is used as evaluation of interval number. Then, integral of all distances is used as evaluation of fuzzy number. Finally, ranking fuzzy numbers is implemented by the evaluations of fuzzy numbers. In order to illustrate the ranking method, numeric example is shown, and for the comparative study, our method is compared with four existing ranking methods. As an example of potential applications, the proposed method is applied to game with Fuzzy Profit.