Well-formed decompositions of Generalized Additive Independence models

Michel Grabisch (1, 2) , Christophe Labreuche (3) , Mustapha Ridaoui (1, 2)

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics
3 Thales Research and Technology [Palaiseau]

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.

Mots clés: Generalized Additive Independence; multichoice game; decision making; decomposition

Domaines: Economies et finances; Mathématique discrète [cs.DM]

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