Monotone decomposition of 2-additive Generalized Additive Independence models

Michel Grabisch and Christophe Labreuche ()
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Christophe Labreuche: Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales) - THALES [France] - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: generalized additive independence; capacity; multicriteria decision making; multichoice game; conjoint measurement (search for similar items in EconPapers)
Date: 2018-03
Note: View the original document on HAL open archive server: https://hal.science/hal-02043268v1
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Citations: View citations in EconPapers (11)

Published in Mathematical Social Sciences, 2018, 92, pp.64-73. ⟨10.1016/j.mathsocsci.2017.09.007⟩

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Related works:
Journal Article: 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:hal:pseptp:hal-02043268

DOI: 10.1016/j.mathsocsci.2017.09.007

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