, Volume 5, Issue 2, pp 117–142 | Cite as

Quadratic distances for capacity and bi-capacity approximation and identification

Regular paper


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.


Multi-attribute utility theory Choquet integral Capacity Bi-capacity Quadratic programming 

MSC Classification

90B50 91B16 90C20 


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Copyright information

© Springer Verlag 2006

Authors and Affiliations

  1. 1.LINA CNRS FRE 2729, Site école polytechnique de l’université de NantesNantesFrance

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