Evaluating the Promethee ii Ranking Quality

Multicriteria decision aid consists in helping decision makers to compare (rank, choose, sort, etc.) different alternatives which are evaluated on conflicting criteria. One well-known family of multicriteria decision aid methods is Promethee. It is based on pairwise comparisons of the alternatives to produce a complete or a partial ranking. Promethee is widely used in practical applications, and different aspects of its theoretical properties have already been studied in the literature. However, no work has been proposed to assess the quality of the rankings it produces with regard to the pairwise preference matrix it exploits. This work addresses this problem by proposing a new indicator of the quality of the rankings produced by Promethee ii. This indicator is derived from a new property of the net flow score procedure. The indicator is illustrated on both artificial and real datasets.