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AbstractMulticriteria decision aid consists of helping decision makers to compare (rank, choose, sort, etc.) different alternatives which are evaluated on conflicting criteria. In the last decades, numerous decision aid methods have been developed. Three main categories of decision aid methods are usually considered: the aggregating, interactive and outranking methods. While aggregation methods produce a complete ranking of the set of alternatives, outranking methods usually allow some pairs of alternatives to remain incomparable. This happens either if the two alternatives present some strong conflicting information or if there are not enough elements in the decision problem to state the preference or indifference between them. A well‐known family of outranking procedures are the Promethee methods. The aim of this work is first to provide an analysis of the incomparability relation produced by Promethee I. From our point of view, some shortcomings of this incomparability relation are presented. Then, a new method based on the comparison of weighted coalitions of mono‐criterion net flow score differences, called Promethee , is proposed. Promethee and Promethee i are then further compared.

AbstractSo far, the rank reversal (RR) phenomenon has been heavily discussed in the multiple criteria analysis literature. In this work, instead of focusing on RR occurrences within PROMETHEE II, an analysis of the third alternative with respect to a given pair of alternatives is conducted. The aim is to provide a way to identify third alternatives able to cause RR between a specific pair. This opens the question of building alternatives causing RR occurrences. Such alternatives can then be used to assess the resistance a given ranking has to RR. In the end, two different approaches are used. The first considers the number of third alternatives to be added to generate RR for a given pair of alternatives. While, the second one, provides a new threshold for RR occurrences in PROMETHEE II.

AbstractPromethee ii is a multi‐criteria decision aid method working as follows: firstly, all alternatives are compared two by two to form a pairwise comparison matrix. Then the net flow score procedure is applied on this matrix to assign a score to each alternative according to which they are ranked. Methods of the Promethee family may suffer from rank reversal occurrences. The legitimacy of methods suffering from this phenomenon has been largely debated in the literature. The aim of this work is to provide a characterization of the Promethee ii net flow scores as a combination between two distinct methods based on different hypotheses. The first one is based on the direct pairwise comparison of the two considered alternatives while the second is based on the comparison with respect to all the other alternatives of the problem. This combination highlights the dependence on third alternatives as an inherent characteristic of the Promethee ii method.