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Theoretical Drawbacks in Fuzzy Ranking Methods and Some Suggestions for a Meaningful Comparison: An Application to Fuzzy Risk Analysis

ABSTRACT Comparing fuzzy numbers has become one of the key challenging issues in fuzzy sets. Many researchers have proposed different procedures to rank fuzzy numbers, but the results frequently contradict each other. This work addresses the key weakness of several fuzzy ranking methods which have been introduced in recent articles. In this paper, we reveal that in nearly all ranking methods that the ranking procedure depends on the height of fuzzy numbers the result is unreliable. However, the final aim of this study is to propose some suggestions for a meaningful comparison in new methods. We demonstrate our reasoning with several numerical cases taken from literature.