A Preference Index for Ranking Closed Intervals and Fuzzy Numbers

This paper proposes a preference index for ranking the most applicable vague data, i.e. closed intervals and LR-fuzzy numbers. In this approach, first a preference degree is suggested to compare two closed intervals. Then, we extended the proposed criterion from the space of closed intervals into the the space of fuzzy numbers. Using some theorems and lemmas, it will be proved that the extended preference degrees will satisfy many common and desired properties based on the proposed axiomatic definitions introduced for similarity measures. Some numerical examples are also used to illustrate the proposed ranking methods. Moreover, the proposed methods are examined to compare other existing methods and the feasibility and effectiveness of the proposed methods will be cleared via some numerical comparisons. Comparative examples show that the proposed method overcomes certain unreasonable and shortcomings exhibited by some existing methods in some common situations.