Monotone decomposition of 2-additive Generalized Additive Independence models

Abstract : 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.
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Contributor : Michel Grabisch <>
Submitted on : Wednesday, February 20, 2019 - 6:56:32 PM
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Michel Grabisch, Christophe Labreuche. Monotone decomposition of 2-additive Generalized Additive Independence models. Mathematical Social Sciences, Elsevier, 2018, 92, pp.64-73. ⟨10.1016/j.mathsocsci.2017.09.007⟩. ⟨hal-02043268⟩

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