Fuzzy Risk Analysis Based on Ranking of Fuzzy Numbers Via New Magnitude Method

Abstract

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