# The Choquet integral as a linear interpolator

1 DECISION
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We show that the Choquet integral is the unique linear interpolator between vertices of the $[0, 1]^n$ hypercube, using the least possible number of vertices. Related results by Lovasz and Singer are discussed, as well as other interpolations. We show that the Choquet integral for bi-capacities can be also casted into this framework. Lastly, we discuss the case of Sugeno integral.
Type de document :
Communication dans un congrès
IPMU 2004 - 10th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Jul 2004, Perugia, Italy. IPMU 2004 - 10th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp.373-378
Domaine :
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https://hal.archives-ouvertes.fr/hal-01496293
Contributeur : Lip6 Publications <>
Soumis le : lundi 27 mars 2017 - 13:39:19
Dernière modification le : lundi 17 décembre 2018 - 01:25:00

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• HAL Id : hal-01496293, version 1

### Citation

Michel Grabisch. The Choquet integral as a linear interpolator. IPMU 2004 - 10th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Jul 2004, Perugia, Italy. IPMU 2004 - 10th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp.373-378. 〈hal-01496293〉

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