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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 = Université de Gand)

  • 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-03904412v1
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    References listed on IDEAS

    as
    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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    6. 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.
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    9. Denis Bouyssou & Marc Pirlot, 2002. "Nontransitive Decomposable Conjoint Measurement," Post-Print hal-02361942, HAL.
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    11. 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.
    12. Denis Bouyssou & Marc Pirlot, 2016. "Conjoint Measurement Tools for MCDM," 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 97-151, Springer.
    13. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02917994, HAL.
    14. 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.
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    16. 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.
    17. 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.
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    23. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2020. "A theoretical look at ELECTRE TRI-nB," Working Papers hal-02898131, HAL.
    24. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2019. "The size of the largest antichains in products of linear orders," Working Papers hal-02398393, HAL.
    25. Salvatore Greco & Benedetto Matarazzo & Roman Słowinński, 2005. "Decision Rule Approach," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 507-555, Springer.
    26. Mousseau, Vincent & Dias, Luis, 2004. "Valued outranking relations in ELECTRE providing manageable disaggregation procedures," European Journal of Operational Research, Elsevier, vol. 156(2), pages 467-482, July.
    27. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2004. "Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules," European Journal of Operational Research, Elsevier, vol. 158(2), pages 271-292, October.
    28. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "The size of the maximum antichains in products of linear orders," Post-Print hal-03047087, HAL.
    29. 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. 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.
    2. 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.
    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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