Multiple criteria sorting with a set of additive value functions

Salvatore Greco (1) , Vincent Mousseau (2) , Roman Slowinski (3)

1 Unict - Università degli studi di Catania = University of Catania
2 LGI - Laboratoire Génie Industriel - EA 2606
3 IDSS Lab - Intelligent Decision Support System Laboratory

We present a new multiple criteria sorting method that aims at assigning actions eval- uated on multiple criteria to p pre-defined ordered classes. The preference information supplied by the decision maker (DM) is a set of assignment examples concerning reference actions. Each assignment example specifies a desired assignment for a reference action to one or several contiguous classes. The assignment examples used to build a preference model based on a set of general additive compatible value functions. For each compatible value function one can associate a set of p−1 thresholds on the value function separating consecutive classes. For each action a, the method computes two kinds of assignments to classes, concordant with the DM's preference model. The necessary assignment specifies the range of classes to which the action can be assigned considering all compatible value functions simultaneously. The possible assignment specifies, in turn, the range of classes to which the action can be assigned considering any compatible value functions individ- ually. The compatible value functions and the necessary and possible assignments are computed through the resolution of linear programs. Based on the concepts of necessary and possible assignments, an interactive methodology is proposed, and illustrated on a real world example

Mots clés: Multiple criteria sorting; Additive value function; Disaggregation-aggregation procedure

Domaines: Recherche opérationnelle [math.OC]

Salvatore Greco, Vincent Mousseau, Roman Slowinski. Multiple criteria sorting with a set of additive value functions. 2008. ⟨hal-00906932⟩