A comparison of the GAI model and the Choquet integral with respect to a k-ary capacity

Christophe Labreuche () and Michel Grabisch
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: Two utility models are classically used to represent interaction among criteria: the Choquet integral and the Generalized Additive Independence (GAI) model. We propose a comparison of these models. Looking at their mathematical expression, it seems that the second one is much more general than the first one. The GAI model has been mostly studied in the case where attributes are discrete. We propose an extension of the GAI model to continuous attributes, using the multi-linear interpolation. The values that are interpolated can in fact be interpreted as a k-ary capacity, or its extension – called p-ary capacity – where p is a vector and pi is the number of levels attached to criterion i. In order to push the comparison further, the Choquet integral with respect to a p-ary capacity is generalized to preferences that are not necessarily monotonically increasing or decreasing on the attributes. Then the Choquet integral with respect to a p-ary capacity differs from a GAI model only by the type of interpolation model. The Choquet integral is the Lovász extension of a p-ary capacity whereas the GAI model is the multi-linear extension of a p-ary capacity

Keywords: Multiple criteria analysis; Generalized Additive Independence; Choquet integral; interpolation (search for similar items in EconPapers)
JEL-codes: C44 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2016-01
New Economics Papers: this item is included in nep-upt
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
ftp://mse.univ-paris1.fr/pub/mse/CES2016/16004.pdf (application/pdf)

Related works:
Working Paper: A comparison of the GAI model and the Choquet integral with respect to a k-ary capacity (2016)
Working Paper: A comparison of the GAI model and the Choquet integral with respect to a k-ary capacity (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:16004

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 ().