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Well-formed decompositions of Generalized Additive Independence models

Michel Grabisch, Christophe Labreuche () and Mustapha Ridaoui ()
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Christophe Labreuche: Thales Research and Technology [Palaiseau] - THALES
Mustapha Ridaoui: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: Generalized Additive Independence (GAI) models permit to represent interacting variables in decision making. A fundamental problem is that the expression of a GAI model is not unique as it has several equivalent different decompositions involving multivariate terms. Considering for simplicity 2-additive GAI models (i.e., with multivariate terms of at most 2 variables), the paper examines the different questions (definition, monotonicity, interpretation, etc.) around the decomposition of a 2-additive GAI model and proposes as a basis the notion of well-formed decomposition. We show that the presence of a bi-variate term in a well-formed decomposition implies that the variables are dependent in a preferential sense. Restricting to the case of discrete variables, and based on a previous result showing the existence of a monotone decomposition, we give a practical procedure to obtain a monotone and well-formed decomposition and give an explicit expression of it in a particular case.

Keywords: decomposition; decision making; multichoice game; Generalized Additive Independence (search for similar items in EconPapers)
Date: 2020
New Economics Papers: this item is included in nep-dcm
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-03022926
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Published in Annals of Operations Research, Springer Verlag, inPress

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Working Paper: Well-formed decompositions of Generalized Additive Independence models (2020) Downloads
Working Paper: Well-formed decompositions of Generalized Additive Independence models (2020) Downloads
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