Monotone decomposition of 2-additive Generalized Additive Independence models

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

1 CES - Centre d'économie de la Sorbonne
2 PSE - Paris School of Economics
3 Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales)

The GAI (Generalized Additive Independence) model proposed by Fishburn is a generalization of the additive value function model, which need not satisfy preferential independence. Its great generality makes however its application and study difficult. We consider a significant subclass of GAI models, namely the discrete 2-additive GAI models, and provide for this class a decomposition into nonneg-ative monotone terms. This decomposition allows a reduction from exponential to quadratic complexity in any optimization problem involving discrete 2-additive models, making them usable in practice.

Mots clés: generalized additive independence; capacity; multicriteria decision making; multichoice game; conjoint measurement

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

Michel Grabisch, Christophe Labreuche. Monotone decomposition of 2-additive Generalized Additive Independence models. Mathematical Social Sciences, 2018, 92, pp.64-73. ⟨10.1016/j.mathsocsci.2017.09.007⟩. ⟨hal-02043268⟩