Monotone decomposition of 2-additive Generalized Additive Independence models

Michel Grabisch and Christophe Labreuche

Mathematical Social Sciences, 2018, vol. 92, issue C, 64-73

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 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.

Date: 2018
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Related works:
Working Paper: Monotone decomposition of 2-additive Generalized Additive Independence models (2018)
Working Paper: Monotone decomposition of 2-additive Generalized Additive Independence models (2018)
Working Paper: Monotone decomposition of 2-additive Generalized Additive Independence models (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:92:y:2018:i:c:p:64-73

DOI: 10.1016/j.mathsocsci.2017.09.007

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