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
Mustapha Ridaoui: Université Paris I - Panthéon-Sorbonne

Annals of Operations Research, 2022, vol. 312, issue 2, No 8, 827-852

Abstract: 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: Generalized additive independence; Multichoice game; Decision making; Decomposition (search for similar items in EconPapers)
Date: 2022
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Working Paper: Well-formed decompositions of Generalized Additive Independence models (2022)
Working Paper: Well-formed decompositions of Generalized Additive Independence models (2022)
Working Paper: Well-formed decompositions of Generalized Additive Independence models (2022)
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DOI: 10.1007/s10479-020-03844-w

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