Hierarchies consistency analysis for nontransitive problems

By assuming different hierarchies—or different hierarchy structures—for the same problem should yield the same aggregated performance index, an approach can be developed for evaluating the performance of multiple level and multiple criteria problems. This proposed approach has the advantage that it is completely based on a rational index and no requirement of transitivity is needed. Furthermore, the analyses of different criteria structures give further insights about the problem being considered. The disadvantage is, of course, we must assume that different hierarchies must yield the same aggregate performance index, which is not generally true for all problems under all conditions.