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Multi-criteria decision making via multivariate quantiles

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  • Daniel Kostner

    (Free University of Bozen-Bolzano)

Abstract

A novel approach for solving a multiple judge, multiple criteria decision making (MCDM) problem is proposed. The presence of multiple criteria leads to a non-total order relation. The ranking of the alternatives in such a framework is done by reinterpreting the MCDM problem as a multivariate statistics one and by applying the concepts in Hamel and Kostner (J Multivar Anal 167:97–113, 2018). A function that ranks alternatives as well as additional functions that categorize alternatives into sets of “good” and “bad” choices are presented. The paper shows that the properties of these functions ensure a reasonable decision making process.

Suggested Citation

  • Daniel Kostner, 2020. "Multi-criteria decision making via multivariate quantiles," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 73-88, February.
    • Handle: RePEc:spr:mathme:v:91:y:2020:i:1:d:10.1007_s00186-019-00675-9
    DOI: 10.1007/s00186-019-00675-9
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    References listed on IDEAS

    as
    1. Hamel, Andreas H. & Kostner, Daniel, 2018. "Cone distribution functions and quantiles for multivariate random variables," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 97-113.
    2. Michel Grabisch, 2016. "Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 301-326, July.
    3. repec:hal:pseose:hal-01372858 is not listed on IDEAS
    4. Michel Grabisch, 2016. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, December.
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    Cited by:

    1. Asmerilda Hitaj & Elisa Mastrogiacomo & Matteo Rocca & Marco Tarsia, 2025. "Robust Multivariate Quantiles in Ranking Problems," Group Decision and Negotiation, Springer, vol. 34(6), pages 1527-1570, December.
    2. Hamel, Andreas H. & Kostner, Daniel, 2022. "Computation of quantile sets for bivariate ordered data," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).

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