A new threshold for the detection of possible rank reversal occurrences in PROMETHEE II rankings

Abstract

Multicriteria decision aid consists in helping decision-makers to compare (rank, choose, sort, etc.) different alternatives which are evaluated on conflicting criteria. A well-known family of decision aid methods is the PROMETHEE family. It has been highlighted that these methods may suffer from rank reversal occurrences. However, Mareschal et al. and later Verly and De Smet have pointed out that rank reversal could only occur between alternatives having similar flow scores. In this work, a stricter threshold on the difference of net flow scores is proposed. It is shown using real datasets that the new threshold significantly reduces the pairs of alternatives subject to rank reversal. A comparison of the different thresholds according to the information on which they are based is also given. These new insights suggest carefully reconsidering the definition of the indifference and the incomparability relation in the context of PROMETHEE methods.