On the decomposition of Generalized Additive Independence models
Discrete Mathematics
2016-01-25 v1
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.
Cite
@article{arxiv.1601.05978,
title = {On the decomposition of Generalized Additive Independence models},
author = {Michel Grabisch and Christophe Labreuche},
journal= {arXiv preprint arXiv:1601.05978},
year = {2016}
}