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A theoretical look at ELECTRE TRI-nB

Author

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  • Denis Bouyssou

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Thierry Marchant

    (Department of Data Analysis - UGENT - Universiteit Gent = Ghent University = Université de Gand)

  • Marc Pirlot

    (Faculté polytechnique de Mons - UMONS - Université de Mons / University of Mons)

Abstract

ELECTRE TRI is a set of methods designed to sort alternatives evaluated on several attributes into ordered categories. The original ELEC-TRE TRI-B method uses one limiting profile per category. A more recent method, ELECTRE TRI-nB, allows one to use several limiting profiles for each category. We investigate the properties of ELECTRE TRI-nB. When the number of limiting profiles used to define each category is not restricted, ELECTRE TRI-nB is easy to characterize axiomatically and is found to be equivalent to several other methods proposed in the literature. We extend this result in various directions.

Suggested Citation

  • Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02898131, HAL.
    • Handle: RePEc:hal:wpaper:hal-02898131
    Note: View the original document on HAL open archive server: https://hal.science/hal-02898131v2
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    References listed on IDEAS

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    1. Salvatore Greco & Benedetto Matarazzo & Roman Słowiński, 2016. "Decision Rule Approach," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 497-552, Springer.
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    8. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    9. Bouyssou, Denis & Marchant, Thierry, 2015. "On the relations between ELECTRE TRI-B and ELECTRE TRI-C and on a new variant of ELECTRE TRI-B," European Journal of Operational Research, Elsevier, vol. 242(1), pages 201-211.
    10. Almeida-Dias, J. & Figueira, J.R. & Roy, B., 2010. "Electre Tri-C: A multiple criteria sorting method based on characteristic reference actions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 565-580, August.
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    13. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2019. "The size of the largest antichains in products of linear orders," Working Papers hal-02398393, HAL.
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    Cited by:

    1. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2023. "A theoretical look at Electre Tri-nB and related sorting models," 4OR, Springer, vol. 21(1), pages 1-31, March.
    2. Eduardo Fernandez & Jorge Navarro & Efrain Solares, 2021. "A theoretical look at ordinal classification methods based on reference sets composed of characteristic actions," Papers 2107.04656, arXiv.org.
    3. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "The size of the maximum antichains in products of linear orders," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 648-659, October.
    4. Tlili, Ali & Belahcène, Khaled & Khaled, Oumaima & Mousseau, Vincent & Ouerdane, Wassila, 2022. "Learning non-compensatory sorting models using efficient SAT/MaxSAT formulations," European Journal of Operational Research, Elsevier, vol. 298(3), pages 979-1006.
    5. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "The size of the maximum antichains in products of linear orders," Post-Print hal-03047087, HAL.

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