Promethee γ: A new Promethee based method for partial ranking based on valued coalitions of monocriterion net flow scores

Multicriteria 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 $\gamma$, is proposed. Promethee $\gamma$ and Promethee i are then further compared.