A Method For Ranking Fuzzy Numbers And Its Application

The indistinct properties is a kind of attribute which the matter exists.With the development of the fuzzy theory ,there are more and more domains which need to be ranked and there are more and more papers on the ranking fuzzy numbers[43]. There have been about 40 kinds of ranking methods proposed in recent years.These methods can be divided into three classes.The first is transform the fuzzy numbers into the real numbers.The second is setting a comparing set at first,then comparing them with the comparing set and determining a ranking relation.The third is setting a fuzzy relation between the fuzzy numbers and comparing them by the fuzzy relation.The three kinds of methods are all determining the relation by setting and dealing with the fuzzy index [42] .However ,because there has not a good method admitted by people by now,someone is still to propose some new methods.In the first half of 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 1 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.