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arXiv · 1601.05978

On the decomposition of Generalized Additive Independence models

Michel Grabisch·Christophe Labreuche
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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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Michel Grabisch, Christophe Labreuche. 2016-01-22. On the decomposition of Generalized Additive Independence models. https://arxiv.org/abs/1601.05978

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