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Monotone decomposition of 2-additive Generalized Additive Independence models

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  • Grabisch, Michel
  • Labreuche, Christophe

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.

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  • Grabisch, Michel & Labreuche, Christophe, 2018. "Monotone decomposition of 2-additive Generalized Additive Independence models," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 64-73.
    • Handle: RePEc:eee:matsoc:v:92:y:2018:i:c:p:64-73
    DOI: 10.1016/j.mathsocsci.2017.09.007
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    1. Greco, Salvatore & Mousseau, Vincent & Słowiński, Roman, 2014. "Robust ordinal regression for value functions handling interacting criteria," European Journal of Operational Research, Elsevier, vol. 239(3), pages 711-730.
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    3. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    4. Miranda, P. & Combarro, E.F. & Gil, P., 2006. "Extreme points of some families of non-additive measures," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1865-1884, November.
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    6. Michel Grabisch & Jacques Duchene & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Positions," Post-Print halshs-00273179, HAL.
    7. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
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    Cited by:

    1. GRABISCH, Michel & LABREUCHE, Christophe & RIDAOUI, Mustapha, 2019. "On importance indices in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 277(1), pages 269-283.
    2. Michel Grabisch & Christophe Labreuche & Mustapha Ridaoui, 2022. "Well-formed decompositions of generalized additive independence models," Annals of Operations Research, Springer, vol. 312(2), pages 827-852, May.
    3. Labreuche, Christophe & Grabisch, Michel, 2018. "Using multiple reference levels in Multi-Criteria Decision aid: The Generalized-Additive Independence model and the Choquet integral approaches," European Journal of Operational Research, Elsevier, vol. 267(2), pages 598-611.

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