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A theoretical look at Electre Tri-nB and related sorting models

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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

    (UGENT - Universiteit Gent = Ghent University)

  • Marc Pirlot

Abstract

Electre Tri is a set of methods designed to sort alternatives evaluated on several criteria into ordered categories. In these methods, alternatives are assigned to categories by comparing them with reference profiles that represent either the boundary or central elements of the category. The original Electre Tri-B method uses one limiting profile for separating a category from the category below. A more recent method, Electre Tri-nB, allows one to use several limiting profiles for the same purpose. We investigate the properties of Electre Tri-nB using a conjoint measurement framework. 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2022. "A theoretical look at Electre Tri-nB and related sorting models," Post-Print hal-03904412, HAL.
    • Handle: RePEc:hal:journl:hal-03904412
    DOI: 10.1007/s10288-022-00501-9
    Note: View the original document on HAL open archive server: https://hal.science/hal-03904412
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    References listed on IDEAS

    as
    1. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2010. "Multiple criteria sorting with a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1455-1470, December.
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    6. Denis Bouyssou & Marc Pirlot, 2015. "A consolidated approach to the axiomatization of outranking relations: a survey and new results," Annals of Operations Research, Springer, vol. 229(1), pages 159-212, June.
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    24. Doumpos, M. & Marinakis, Y. & Marinaki, M. & Zopounidis, C., 2009. "An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method," European Journal of Operational Research, Elsevier, vol. 199(2), pages 496-505, December.
    25. Almeida-Dias, J. & Figueira, J.R. & Roy, B., 2012. "A multiple criteria sorting method where each category is characterized by several reference actions: The Electre Tri-nC method," European Journal of Operational Research, Elsevier, vol. 217(3), pages 567-579.
    26. Denis Bouyssou & Marc Pirlot, 2002. "Nontransitive Decomposable Conjoint Measurement," Post-Print hal-02361942, HAL.
    27. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02917994, HAL.
    28. 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.
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    32. Bouyssou, Denis & Marchant, Thierry, 2010. "Additive conjoint measurement with ordered categories," European Journal of Operational Research, Elsevier, vol. 203(1), pages 195-204, May.
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    Cited by:

    1. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2022. "A note on ELECTRE TRI-nB with few limiting profiles," 4OR, Springer, vol. 20(3), pages 443-463, September.
    2. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2023. "Multiple criteria sorting models and methods. Part II: theoretical results and general issues," 4OR, Springer, vol. 21(2), pages 181-204, June.
    3. 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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