Advanced Analysis on the Behavior of PROMETHEE Methods under Independence Property and Some Derived Versions

In this paper, we study the sensitivity of PROMETHEE family methods using four derived versions of Independence property. In particular, we analyse the strangeness of each type of relation (i.e. Indifference, Preference and Incomparability) in the global ranking. On this basis, we establish relevant rules and mathematical conditions upon which PROMETHEE family methods keep their original ranking. In case of change, we propose post-optimality study allowing to expect the new relation between the alternatives while avoiding to process the method. In addition, the intervals of stability of each relation are extracted accordingly. The efficiency of the results is illustrated using numerical examples among what two are real-life cases. Indeed, the first one describes the project of ranking alternatives for the selection of electric buses in Turkey while the second one defines the problem of scheduling decision making within mechanical workshop for tracks construction in Algeria. Finally, a statistical study comparing the impact of the independence versions using PROMETHEE I, II as well as large number of instances is established.