IDEAS home Printed from https://ideas.repec.org/p/hal/journl/halshs-01222546.html
   My bibliography  Save this paper

On the decomposition of Generalized Additive Independence models

Author

Listed:
  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • 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)

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.

Suggested Citation

  • Michel Grabisch & Christophe Labreuche, 2015. "On the decomposition of Generalized Additive Independence models," Post-Print halshs-01222546, HAL.
    • Handle: RePEc:hal:journl:halshs-01222546
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01222546
    as

    Download full text from publisher

    File URL: https://shs.hal.science/halshs-01222546/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    2. 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.
    3. Ali E. Abbas & Zhengwei Sun, 2015. "Multiattribute Utility Functions Satisfying Mutual Preferential Independence," Operations Research, INFORMS, vol. 63(2), pages 378-393, April.
    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.
    5. James S. Dyer & Rakesh K. Sarin, 1979. "Measurable Multiattribute Value Functions," Operations Research, INFORMS, vol. 27(4), pages 810-822, August.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Grabisch, Michel & Labreuche, Christophe, 2018. "Monotone decomposition of 2-additive Generalized Additive Independence models," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 64-73.
    2. Christophe Labreuche & Michel Grabisch, 2016. "A comparison of the GAI model and the Choquet integral with respect to a k-ary capacity," Documents de travail du Centre d'Economie de la Sorbonne 16004, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    3. Mayag, Brice & Bouyssou, Denis, 2020. "Necessary and possible interaction between criteria in a 2-additive Choquet integral model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 308-320.
    4. 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.
    5. Haag, Fridolin & Lienert, Judit & Schuwirth, Nele & Reichert, Peter, 2019. "Identifying non-additive multi-attribute value functions based on uncertain indifference statements," Omega, Elsevier, vol. 85(C), pages 49-67.
    6. Ferreira, João J.M. & Jalali, Marjan S. & Ferreira, Fernando A.F., 2018. "Enhancing the decision-making virtuous cycle of ethical banking practices using the Choquet integral," Journal of Business Research, Elsevier, vol. 88(C), pages 492-497.
    7. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
    8. Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio, 2016. "Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression," Omega, Elsevier, vol. 61(C), pages 2-18.
    9. 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.
    10. Silvia Angilella & Marta Bottero & Salvatore Corrente & Valentina Ferretti & Salvatore Greco & Isabella M. Lami, 2016. "Non Additive Robust Ordinal Regression for urban and territorial planning: an application for siting an urban waste landfill," Annals of Operations Research, Springer, vol. 245(1), pages 427-456, October.
    11. Salvatore Corrente & José Figueira & Salvatore Greco, 2014. "Dealing with interaction between bipolar multiple criteria preferences in PROMETHEE methods," Annals of Operations Research, Springer, vol. 217(1), pages 137-164, June.
    12. Bilbao-Terol, Amelia & Bilbao-Terol, Celia, 2024. "The Choquet integral supported by a hedonic approach for modelling preferences in hotel selection," Omega, Elsevier, vol. 122(C).
    13. Zhao Qiaojiao & Zeng Ling & Liu Jinjin, 2016. "Fuzzy Integral Multiple Criteria Decision Making Method Based on Fuzzy Preference Relation on Alternatives," Journal of Systems Science and Information, De Gruyter, vol. 4(3), pages 280-290, June.
    14. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Post-Print hal-01302377, HAL.
    15. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2009. "A characterization of the 2-additive Choquet integral through cardinal information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445132, HAL.
    16. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2015. "Dealing with a multiple criteria environmental problem with interaction effects between criteria through an extension of the Electre III method," European Journal of Operational Research, Elsevier, vol. 245(3), pages 837-850.
    17. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.
    18. Michel Grabisch & Christophe Labreuche, 2019. "Interpretation of multicriteria decision making models with interacting criteria," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381243, HAL.
    19. Peter Reichert & Klemens Niederberger & Peter Rey & Urs Helg & Susanne Haertel-Borer, 2019. "The need for unconventional value aggregation techniques: experiences from eliciting stakeholder preferences in environmental management," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 197-219, November.
    20. 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.

    More about this item

    Keywords

    Multiattribute utility; Multichoice games; Utilité multi-attribut; jeux multichoix;
    All these keywords.

    JEL classification:

    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:journl:halshs-01222546. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.