A New Approach for Ranking Fuzzy Numbers

In many fuzzy decision problems, ranking fuzzy numbers is an important procedure. Because of the imperfection and fuzziness of thinking, we need a method to compare fuzzy numbers. So far, a great deal of research has been obtained. Some of them use the centroid point of fuzzy numbers as an index to rank the fuzzy numbers. Having reviewed the previous researches, we found that almost each of them tried to use a formula to rank the fuzzy numbers. However, most of them hardly can rank with intuition consistently in all cases. Therefore, a new method of ranking fuzzy numbers is proposed and compensates for these shortcomings. It uses three indices to differentiate between fuzzy numbers. The representation location of fuzzy number A is a top priority. The place that the largest membership function grade happened is the second. And then is S(subscript A) which means the remainder area is the last. Finally, efficiency and superiority of the proposed method are illustrated by some numerical examples.