advanced analysis on the behavior of promethee methods under independence property and some derived versions

This paper investigates the sensitivity of the multicriteria decision making methods: promethee family, based on four different versions of the independence property. the analysis focuses on the robustness of each binary relation between alternatives, i.e. indifference, preference and incomparability in the overall ranking. from this optic, relevant mathematical rules and conditions are established to ensure that promethee methods maintain their initial ranking. in case of variation, a post-optimality study is proposed to anticipate the new relation without requiring a reconsideration of the method. in addition, stability intervals for each specific relation are extracted accordingly. the effectiveness of the results is demonstrated through numerical examples, two of which come from real life cases. the first deals with a project to rank alternatives for the selection of electric buses in turkey, while the second addresses a decision-making problem linked to scheduling in a mechanical workshop for track construction in algeria. finally, a statistical analysis is established to compare the impact of different versions of independence using promethee i and ii.