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Additive conjoint measurement with ordered categories

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

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

Abstract
Conjoint measurement studies binary relations defined on product sets and investigates the existence and uniqueness of, usually additive, numerical representations of such relations. It has proved to be quite a powerful tool to analyze and compare MCDM techniques designed to build a preference relation between multiattributed alternatives and has been an inspiring guide to many assessment protocols. The aim of this paper is to show that additive representations can be obtained on the basis of much poorer information than a preference relation. We will suppose here that the decision maker only specifies for each object if he/she finds it "attractive" (better than the status quo), "unattractive" (worse than the status quo) or "neutral" (equivalent to the status quo). We show how to build an additive representation, with tight uniqueness properties, using such an ordered partition of the set of objects. On a theoretical level, this paper shows that classical results of additive conjoint measurement can be extended to cover the case of ordered partitions and wishes to be a contribution to the growing literature on the foundations of sorting techniques in MCDM. On a more practical level, our results suggest an assessment strategy of an additive model on the basis of an ordered partition.
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Suggested Citation

  • Denis Bouyssou & Thierry Marchant, 2010. "Additive conjoint measurement with ordered categories," Post-Print hal-02359818, HAL.
    • Handle: RePEc:hal:journl:hal-02359818
    DOI: 10.1016/j.ejor.2009.07.032
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    References listed on IDEAS

    as
    1. 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.
    2. Vind, Karl, 1991. "Independent preferences," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 119-135.
    3. Zopounidis, Constantin & Doumpos, Michael, 2002. "Multicriteria classification and sorting methods: A literature review," European Journal of Operational Research, Elsevier, vol. 138(2), pages 229-246, April.
    4. Denis Bouyssou & Thierry Marchant, 2009. "Ordered categories and additive conjoint measurement on connected sets," Post-Print hal-02361900, HAL.
    5. 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.
    6. Chateauneuf, Alain & Wakker, Peter, 1993. "From local to global additive representation," Journal of Mathematical Economics, Elsevier, vol. 22(6), pages 523-545.
    7. Denis Bouyssou & Thierry Marchant & Marc Pirlot & Alexis Tsoukiàs & Philippe Vincke, 2006. "Evaluation and Decision Models with Multiple Criteria," International Series in Operations Research and Management Science, Springer, number 978-0-387-31099-2, December.
    8. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2002. "Rough sets methodology for sorting problems in presence of multiple attributes and criteria," European Journal of Operational Research, Elsevier, vol. 138(2), pages 247-259, April.
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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. Mikhail Timonin, 2016. "Conjoint axiomatization of the Choquet integral for heterogeneous product sets," Papers 1603.08142, arXiv.org.
    4. Denis Bouyssou & Thierry Marchant, 2011. "Subjective expected utility without preferences," Working Papers hal-00606939, HAL.
    5. Salvatore Corrente & Michael Doumpos & Salvatore Greco & Roman Słowiński & Constantin Zopounidis, 2017. "Multiple criteria hierarchy process for sorting problems based on ordinal regression with additive value functions," Annals of Operations Research, Springer, vol. 251(1), pages 117-139, April.
    6. 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.
    7. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "A note on ELECTRE TRI-nB with few limiting profiles," Post-Print hal-02917998, HAL.

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