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How to score alternatives when criteria are scored on an ordinal scale

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  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We address in this paper the problem of scoring alternatives when they are evaluated with respect to several criteria on a finite ordinal scale $E$. We show that in general, the ordinal scale $E$ has to be refined or shrunk in order to be able to represent the preference of the decision maker by an aggregation operator belonging to the family of mean operators. The paper recalls previous theoretical results of the author giving necessary and sufficient conditions for a representation of preferences, and then focusses on describing practical algorithms and examples.

Suggested Citation

  • Michel Grabisch, 2008. "How to score alternatives when criteria are scored on an ordinal scale," Post-Print halshs-00340381, HAL.
    • Handle: RePEc:hal:journl:halshs-00340381
    DOI: 10.1002/mcda.422
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00340381
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    References listed on IDEAS

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    1. Ovchinnikov, Sergei, 1996. "Means on ordered sets," Mathematical Social Sciences, Elsevier, vol. 32(1), pages 39-56, August.
    2. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    3. Massam, Bryan H & Askew, Ian D, 1982. "Methods for comparing policies using multiple criteria: an urban example," Omega, Elsevier, vol. 10(2), pages 195-204.
    4. Agnès Rico & Michel Grabisch & Christophe Labreuche & Alain Chateauneuf, 2005. "Preference modelling on totally ordered sets by the Sugeno integral," Post-Print hal-00268984, HAL.
    5. J. H. P. Paelinck, 1976. "Qualitative Multiple Criteria Analysis, Environmental Protection And Multiregional Development," Papers in Regional Science, Wiley Blackwell, vol. 36(1), pages 59-76, January.
    6. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    7. Patrick Meyer & Marc Roubens, 2005. "Choice, Ranking and Sorting in Fuzzy Multiple Criteria Decision Aid," International Series in Operations Research & Management Science, in: Multiple Criteria Decision Analysis: State of the Art Surveys, chapter 0, pages 471-503, Springer.
    8. 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.
    9. Vansnick, Jean-Claude, 1986. "On the problem of weights in multiple criteria decision making (the noncompensatory approach)," European Journal of Operational Research, Elsevier, vol. 24(2), pages 288-294, February.
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