Well-formed decompositions of Generalized Additive Independence models

Journal article: 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.

Author(s)

Michel Grabisch, Christophe Labreuche, Mustapha Ridaoui

Journal
  • Annals of Operations Research
Date of publication
  • 2022
Keywords
  • Generalized Additive Independence
  • Multichoice game
  • Decision making
  • Decomposition
Pages
  • 827–852
Version
  • 1
Volume
  • 312