Theory and Decision

, Volume 71, Issue 3, pp 297–324

A representation of preferences by the Choquet integral with respect to a 2-additive capacity

  • Brice Mayag
  • Michel Grabisch
  • Christophe Labreuche
Article

DOI: 10.1007/s11238-010-9198-3

Cite this article as:
Mayag, B., Grabisch, M. & Labreuche, C. Theory Decis (2011) 71: 297. doi:10.1007/s11238-010-9198-3

Abstract

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.

Keywords

CapacityMöbius transformChoquet integralMultiple criteria decision analysisk-monotone functionBelief function

Copyright information

© Springer Science+Business Media, LLC. 2010

Authors and Affiliations

  • Brice Mayag
    • 1
    • 2
  • Michel Grabisch
    • 1
  • Christophe Labreuche
    • 2
  1. 1.Centre d’Economie de la SorbonneUniversity of Paris IParisFrance
  2. 2.Thales R & TPalaiseau cedexFrance