On the decomposition of Generalized Additive Independence models

Abstract : The GAI (Generalized Additive Independence) model proposed by Fishburn is a generalization of the additive utility model, which need not satisfy mutual 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 nonnegative 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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Submitted on : Friday, October 30, 2015 - 10:57:52 AM
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Michel Grabisch, Christophe Labreuche. On the decomposition of Generalized Additive Independence models. 2015. ⟨halshs-01222546⟩

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