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A note on ELECTRE TRI-nB with few limiting profiles

Author

Listed:
  • Denis Bouyssou

    (Université Paris-Dauphine, PSL Research University)

  • Thierry Marchant

    (Ghent University)

  • Marc Pirlot

    (Université de Mons)

Abstract

ELECTRE TRI-nB is a method designed to sort alternatives evaluated on several attributes into ordered categories. It is an extension of ELECTRE TRI-B that uses several limiting profiles, instead of one, to delimit each category. In a previous paper we have characterized the ordered partitions that can be obtained with ELECTRE TRI-nB, using a simple axiom called linearity. The simplicity of this characterization crucially rests 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 the investigation of such models. We specifically study the case of models using one or two profiles together with an outranking relation based on unanimity.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aqjoor:v:20:y:2022:i:3:d:10.1007_s10288-021-00485-y
    DOI: 10.1007/s10288-021-00485-y
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    References listed on IDEAS

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    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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