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Well-formed decompositions of Generalized Additive Independence models

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.
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https://halshs.archives-ouvertes.fr/halshs-03022926
Contributor : Michel Grabisch <>
Submitted on : Wednesday, November 25, 2020 - 9:17:43 AM
Last modification on : Wednesday, December 2, 2020 - 3:22:26 AM

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  • HAL Id : halshs-03022926, version 1

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Michel Grabisch, Christophe Labreuche, Mustapha Ridaoui. Well-formed decompositions of Generalized Additive Independence models. Annals of Operations Research, Springer Verlag, In press. ⟨halshs-03022926⟩

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