A generalized model for ranking fuzzy sets

A new, generalized approach for the ranking of n fuzzy numbers has been developed based on compatibility measures. Many existing ranking proposals are specific examples of the generalized method determined by the compatibility measure used. For each pair of the n fuzzy numbers to be ordered, the method determines the fuzzy minimum and the fuzzy maximum of the pair and measures the compatibility of each number in the pair to the pair´s fuzzy minimum and maximum. A fuzzy number´s compatibility to the fuzzy minimum represents its degree of being the smaller of the two; likewise, its compatibility to the fuzzy maximum represents its degree of being the larger of the two. From the pairwise rankings a total ordering can be obtained for the n fuzzy numbers. The relation of other ranking methods to each other and how the compatibility-based ranking method generalizes these approaches are presented