Ranking methods based on the dominance degree. An investigation of rank reversal

Abstract

Multi-criteria decision making methods have been used in many applications to derive a ranking of objects evaluated on several criteria. In case these evaluations are imprecise, integrating imprecision in the overall assessment is a further issue. In this paper, we deal with imprecise evaluations in the form of intervals. Therefore, the problem is to rank multi-dimensional interval data.

In recent years, a scoring method using the dominance degree has been proposed in order to rank interval data. This index is ordinal in the sense that it takes only into account the ordering of the endpoints of the evaluation intervals. It is computed by considering the evaluations of all the other objects to be ranked. This implies that the dominance degree, hence the ranking, may change when the set of objects to be ranked is altered. This phenomenon is known as rank reversal in the literature.

We analyze the occurrence of rank reversal when we remove an object from (or add one to) the set of objects to be ranked. We introduce variants of the dominance degree rule and analyze them similarly. This is done both analytically and by simulation. We then compare the dominance degree approach with an adaptation of the Borda rule. We also examine how the presence of a set of reference points can reduce the rank reversal phenomenon and enhance the discrimination power of the method.