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Quadratic distances for capacity and bi-capacity approximation and identification

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Abstract

The application of multi-attribute utility theory based on the Choquet integral requires the prior identification of a capacity if the utility scale is unipolar, or of a bi-capacity if the utility scale is bipolar. In order to implement a minimum distance principle for capacity or bi-capacity approximation or identification, quadratic distances between capacities and bi-capacities are studied. The proposed approach, consisting in solving a strictly convex quadratic program, has been implemented within the GNU R kappalab package for capacity and nonadditive integral manipulation. Its application is illustrated on two examples.

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  1. LINA CNRS FRE 2729, Site école polytechnique de l’université de Nantes, Rue Christian Pauc, 44306, Nantes, France

    Ivan Kojadinovic

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  1. Ivan Kojadinovic
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Kojadinovic, I. Quadratic distances for capacity and bi-capacity approximation and identification. 4OR 5, 117–142 (2007). https://doi.org/10.1007/s10288-006-0014-4

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  • DOI: https://doi.org/10.1007/s10288-006-0014-4

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