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A note on ELECTRE TRI-nB with few limiting profiles

Author

Listed:
  • 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

    (Faculté polytechnique de Mons - UMons - Université de Mons)

Abstract

ELECTRE TRI-nB is a method designed to sort alternatives evaluated on several attributes among ordered categories. It is an extension of ELEC-TRE TRI-B that uses several limiting profiles, instead of one, to delimit each category. In a companion paper we have characterized the partitions that can be obtained with ELECTRE TRI-nB, using a simple axiom called linearity. The simplicity of this characterization crucially depends on the possibility to use as many limiting profiles as we like to delimit a category. This is not completely realistic and there is a need to study models in which the number of limiting profiles delimiting each category is restricted. This note starts such a study. We investigate the case of ELECTRE TRI-nB models based on unanimity and using no more than two limiting profiles per category. Our results show that the constraints on the number of limiting profiles make the problem difficult.

Suggested Citation

  • Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "A note on ELECTRE TRI-nB with few limiting profiles," Post-Print hal-03904403, HAL.
    • Handle: RePEc:hal:journl:hal-03904403
    DOI: 10.1007/s10288-021-00485-y
    Note: View the original document on HAL open archive server: https://hal.science/hal-03904403v4
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    References listed on IDEAS

    as
    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. 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.
    3. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
    4. Vind, Karl, 1991. "Independent preferences," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 119-135.
    5. Bouyssou, Denis & Marchant, Thierry, 2010. "Additive conjoint measurement with ordered categories," European Journal of Operational Research, Elsevier, vol. 203(1), pages 195-204, May.
    6. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "A theoretical look at ELECTRE TRI-nB and related sorting models," Working Papers hal-03157337, HAL.
    7. Denis Bouyssou & Thierry Marchant, 2009. "Ordered categories and additive conjoint measurement on connected sets," Post-Print hal-02361900, HAL.
    8. 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.

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