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

Document Type: Research Paper

Author

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.

Keywords


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