A study of set-theoretic measures for use with the generalized compatibility-based ranking method

Many of the earlier proposals for ranking n fuzzy numbers are based on converting a fuzzy number into one crisp real number which automatically ensures a complete ordering. Newer proposals, however, focus on determining a pairwise ranking or preference for all pairs of fuzzy numbers. Then various methods have been used on these pairwise orderings to determine a final order of the n fuzzy numbers. This paper continues an investigation of a generalized approach for ranking methods based on pairwise ranking. Three primary operations on two fuzzy numbers: compatibility measurement, the fuzzy minimum, and the fuzzy maximum are the basis of the generalized ranking method. The influence of the selection of the compatibility measure on the performance of the generalized ranking method is investigated through empirical testing and analysis of well-known test cases