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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.
(This abstract was borrowed from another version of this item.)

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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    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. Mikhail Timonin, 2016. "Conjoint axiomatization of the Choquet integral for heterogeneous product sets," Papers 1603.08142, arXiv.org.
    3. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2024. "A guided tour of multiple criteria sorting models and methods," Annals of Operations Research, Springer, vol. 343(2), pages 785-845, December.
    4. 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.
    5. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "A note on ELECTRE TRI-nB with few limiting profiles," Post-Print hal-02917998, HAL.
    6. 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.
    7. 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.
    8. Denis Bouyssou & Thierry Marchant, 2011. "Subjective expected utility without preferences," Post-Print hal-02359811, HAL.

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