# 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.
Document type :
Conference papers
Domain :

https://hal.archives-ouvertes.fr/hal-01496293
Contributor : Lip6 Publications <>
Submitted on : Monday, March 27, 2017 - 1:39:19 PM
Last modification on : Thursday, March 21, 2019 - 1:11:45 PM

### Identifiers

• 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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