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

Theory and Decision 71 (3):297-324 (2011)
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
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DOI 10.1007/s11238-010-9198-3
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A Mathematical Theory of Evidence.Glenn Shafer - 1976 - Princeton University Press.
Theory of Games and Economic Behavior.John von Neumann & Oskar Morgenstern - 1945 - Journal of Philosophy 42 (20):550-554.

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