Article

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 MayagAffiliated withCentre d’Economie de la Sorbonne, University of Paris IThales R & T Email author 
  • , Michel GrabischAffiliated withCentre d’Economie de la Sorbonne, University of Paris I
  • , Christophe LabreucheAffiliated withThales R & T

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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

Capacity Möbius transform Choquet integral Multiple criteria decision analysis k-monotone function Belief function