About the computation of robust PROMETHEE II rankings: Empirical evidence

Engineering decision problems often involve the simultaneous optimization of several conflicting criteria. Among multicriteria decision aid methods, PROMETHEE has gained a lot of attention during the last three decades. Despite its successful application in different fields, some researchers have pointed out the fact that PROMETHEE does not respect the independence to third alternatives assumption. This leads to the so-called “rank reversal” phenomenon; the relative position of two alternatives may depend on a third one (and so a manipulation threat might exist). In this paper, we propose an alternative method to compute a complete ranking. Inspired by the ideas of robust statistics, we assess the probability of having a given alternative being ranked before another one based on different samplings of the set of alternatives. This allows us to assess a new pairwise comparison matrix that is then exploited by means of net flow scores. We show on an illustrative example that the new method does not suffer from rank reversal (while the PROMETHEE II ranking does).