^{}Mathematics Department, Firoozkooh Branch of Islamic Azad University, Firoozkooh, Iran

Abstract

Ranking fuzzy numbers plays a main role in many applied models in real world and in particular decision-making procedures. In many proposed methods by other researchers may exist some shortcoming. The most commonly used approaches for ranking fuzzy numbers is based on defuzzification method. Many ranking fuzzy numbers cannot discriminate between two symmetric fuzzy numbers with identical core. In 2009, Abbasbandy and Hajjari proposed an approach for ranking normal trapezoidal fuzzy numbers, which computed the magnitude of fuzzy numbers namely ``Mag" method. Then Hajjari extended it for non-normal trapezoidal fuzzy numbers and also for all generalized fuzzy numbers. However, these methods have the weakness that we mentioned above. Moreover, the result is not consistent with human intuition in this case. Therefore, we are going to present a new method to overcome the mentioned weakness. In order to overcome the shortcoming, a new magnitude approach for ranking trapezoidal fuzzy numbers based on minimum and maximum points and the value of fuzzy numbers is given. The new method is illustrated by some numerical examples and in particular, the results of ranking by the proposed method and some common and existing methods for ranking fuzzy numbers is compared to verify the advantages of presented method.

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