A note on the Sobol' indices and interactive criteria

Michel Grabisch and Christophe Labreuche ()
Additional contact information
Christophe Labreuche: Thales Research and Technology

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

Abstract: The Choquet integral and the Owen extension (or multilinear extension) are the most popular tools in multicriteria decision making to take into account the interaction between criteria. It is known that the interaction transform and the Banzhaf interaction transform arise as the average total variation of the Choquet integral and multilinear extension respectively. We consider in this note another approach to define interaction, by using the Sobol' indices which are related to the analysis of variance of a multivariate model. We prove that the Sobol' indices of the multilinear extension gives the square of the Fourier transform, a well-known concept in computer sciences. We also relate the latter to the Banzhaf interaction transform and compute the Sobol' indices for the 2-additive Choquet integral

Keywords: capacity; interaction index; Sobol' index; multilinear extension; Fourier transform (search for similar items in EconPapers)
Pages: 11 pages
Date: 2016-01
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
ftp://mse.univ-paris1.fr/pub/mse/CES2016/16003.pdf (application/pdf)

Related works:
Working Paper: A note on the Sobol' indices and interactive criteria (2017)
Working Paper: A note on the Sobol' indices and interactive criteria (2017)
Working Paper: A note on the Sobol' indices and interactive criteria (2017)
Working Paper: A note on the Sobol' indices and interactive criteria (2016)
Working Paper: A note on the Sobol' indices and interactive criteria (2016)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:mse:cesdoc:16003

Access Statistics for this paper

More papers in Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne Contact information at EDIRC.
Bibliographic data for series maintained by Lucie Label ().