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Conjoint Axiomatization of the Choquet Integral for Heterogeneous Product Sets

  • Mikhail TimoninEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 610)

Abstract

We propose an axiomatization of the Choquet integral model for the general case of a heterogeneous product set \(X = X_1 \times \ldots \times X_n\). In MCDA elements of X are interpreted as alternatives, characterized by criteria taking values from the sets \(X_i\). Previous axiomatizations of the Choquet integral have been given for particular cases \(X = Y^n\) and \(X = \mathbb {R}^n\). However, within multicriteria context such indenticalness, hence commensurateness, of criteria cannot be assumed a priori. This constitutes the major difference of this paper from the earlier axiomatizations. In particular, the notion of “comonotonicity” cannot be used in a heterogeneous structure, as there does not exist a “built-in” order between elements of sets \(X_i\) and \(X_j\). However, such an order is implied by the representation model. Our approach does not assume commensurateness of criteria. We construct the representation and study its uniqueness properties.

Keywords

Choquet integral Decision theory MCDA Multi-criteria decision making 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Queen Mary University of LondonLondonUK

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