Area ranking of fuzzy numbers based on positive and negative ideal points

The maximizing set and minimizing set method is a popular ranking approach for fuzzy numbers, which ranks them based on their left, right and total utilities. This paper presents an alternative ranking approach for fuzzy numbers called area ranking based on positive and negative ideal points, which defines two new alternative indices for the purpose of ranking. The two new indices are defined in terms of a decision maker (DM)ʹs attitude towards risks and the left and the right areas between fuzzy numbers and the two ideal points. It is shown that the area ranking approach has strong discrimination power and can rank fuzzy numbers that are unable to be discriminated by the maximizing set and minimizing set method. It is also shown that the DMʹs attitude towards risks may have a significant impact on the ranking of fuzzy numbers. As a side product, a new defuzzification formula is also developed and discussed.