T. Hajjari - Mathematics Department, Firoozkooh Branch of Islamic Azad University, Firoozkooh, Iran

Ranking fuzzy numbers plays a main role in many applied models inreal world and in particular decision-making procedures. In manyproposed methods by other researchers may exist some shortcoming.The most commonly used approaches for ranking fuzzy numbers isbased on defuzzification method. Many ranking fuzzy numberscannot discriminate between two symmetric fuzzy numbers withidentical core. In ۲۰۰۹, Abbasbandy and Hajjari proposed anapproach for ranking normal trapezoidal fuzzy numbers, whichcomputed the magnitude of fuzzy numbers namely ``Mag" method.Then Hajjari extended it for non-normal trapezoidal fuzzy numbersand also for all generalized fuzzy numbers. However, thesemethods have the weakness that we mentioned above. Moreover, theresult is not consistent with human intuition in this case.Therefore, we are going to present a new method to overcome thementioned weakness. In order to overcome the shortcoming, a newmagnitude approach for ranking trapezoidal fuzzy numbers based onminimum and maximum points and the value of fuzzy numbers isgiven. The new method is illustrated by some numerical examplesand in particular, the results of ranking by the proposed methodand some common and existing methods for ranking fuzzy numbers iscompared to verify the advantages of presented method.

decision-making, Magnitude, Fuzzy numbers, ranking