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

Mayag, Brice; Grabisch, Michel; Labreuche, Christophe (2011), A Representation of preferences by the Choquet integral with respect to a 2-additive capacity, Theory and Decision, 71, 3, p. 297-324. http://dx.doi.org/10.1007/s11238-010-9198-3

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Type
Article accepté pour publication ou publié
Date
2011
Journal name
Theory and Decision
Volume
71
Number
3
Publisher
Springer
Pages
297-324
Publication identifier
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Author(s)
Mayag, Brice
Grabisch, Michel cc
Labreuche, Christophe
Abstract (EN)
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.
Subjects / Keywords
Belief function; k-monotone function; Multiple criteria decision analysis; Choquet integral; Möbius transform; Capacity