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Monotone decomposition of 2-additive Generalized Additive Independence models

Michel Grabisch and Christophe Labreuche ()
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Christophe Labreuche: UMP CNRS/THALES - Unité mixte de physique CNRS/Thalès - THALES - CNRS - Centre National de la Recherche Scientifique

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

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: multichoice game; conjoint measurement; multicriteria decision making; capacity; generalized additive independence (search for similar items in EconPapers)
Date: 2018-03
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-02043268
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Published in Mathematical Social Sciences, Elsevier, 2018, 92, pp.64-73. ⟨10.1016/j.mathsocsci.2017.09.007⟩

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