Well-formed decompositions of Generalized Additive Independence models
Article dans une revue: 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.
Auteur(s)
Michel Grabisch, Christophe Labreuche, Mustapha Ridaoui
Revue
- Annals of Operations Research
Date de publication
- 2022
Mots-clés
- Generalized Additive Independence
- Multichoice game
- Decision making
- Decomposition
Pages
- 827–852
URL de la notice HAL
Version
- 1
Volume
- 312