IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v91y2020i1d10.1007_s00186-019-00675-9.html
   My bibliography  Save this article

Multi-criteria decision making via multivariate quantiles

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-019-00675-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00186-019-00675-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. "Set Functions, Games and Capacities in Decision Making," Theory and Decision Library C, Springer, number 978-3-319-30690-2, December.
    3. 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.
    4. repec:hal:pseose:hal-01372858 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hamel, Andreas H. & Kostner, Daniel, 2022. "Computation of quantile sets for bivariate ordered data," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Ulrich Faigle & Michel Grabisch, 2019. "Least Square Approximations and Linear Values of Cooperative Game," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381231, HAL.
    3. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2018. "An axiomatisation of the Banzhaf value and interaction index for multichoice games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381119, HAL.
    4. Bottero, M. & Ferretti, V. & Figueira, J.R. & Greco, S. & Roy, B., 2018. "On the Choquet multiple criteria preference aggregation model: Theoretical and practical insights from a real-world application," European Journal of Operational Research, Elsevier, vol. 271(1), pages 120-140.
    5. Mayag, Brice & Bouyssou, Denis, 2020. "Necessary and possible interaction between criteria in a 2-additive Choquet integral model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 308-320.
    6. Cinfrignini, Andrea & Petturiti, Davide & Vantaggi, Barbara, 2023. "Dynamic bid–ask pricing under Dempster-Shafer uncertainty," Journal of Mathematical Economics, Elsevier, vol. 107(C).
    7. Ehud Lehrer & Roee Teper, 2020. "Set-valued capacities: multi-agenda decision making," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 233-248, February.
    8. Michel Grabisch & Tomáš Kroupa, 2018. "The core of supermodular games on finite distributive lattices," Documents de travail du Centre d'Economie de la Sorbonne 18010, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. Michel Grabisch, 2016. "Remarkable polyhedra related to set functions, games," Documents de travail du Centre d'Economie de la Sorbonne 16081, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    10. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02372486, HAL.
    11. Pelegrina, Guilherme Dean & Duarte, Leonardo Tomazeli & Grabisch, Michel & Romano, João Marcos Travassos, 2020. "The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification," European Journal of Operational Research, Elsevier, vol. 282(3), pages 945-956.
    12. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Post-Print halshs-02372486, HAL.
    13. repec:hal:pseose:hal-01372858 is not listed on IDEAS
    14. Alexis Poindron, 2019. "A general model of synchronous updating with binary opinions," Documents de travail du Centre d'Economie de la Sorbonne 19024, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    15. Michel Grabisch & Agnieszka Rusinowska, 2020. "k -additive upper approximation of TU-games," PSE-Ecole d'économie de Paris (Postprint) halshs-02860802, HAL.
    16. Takao Asano & Hiroyuki Kojima, 2022. "Choquet Integrals and Belief Functions," KIER Working Papers 1077, Kyoto University, Institute of Economic Research.
    17. Andreas H. Hamel & Frank Heyde, 2021. "Set-Valued T -Translative Functions and Their Applications in Finance," Mathematics, MDPI, vol. 9(18), pages 1-33, September.
    18. Dylan Laplace Mermoud, 2023. "Geometry of Set Functions in Game Theory: Combinatorial and Computational Aspects," Papers 2301.02950, arXiv.org, revised Oct 2023.
    19. Elisa Mastrogiacomo & Matteo Rocca, 2021. "Set optimization of set-valued risk measures," Annals of Operations Research, Springer, vol. 296(1), pages 291-314, January.
    20. Khaled Belahcène & Vincent Mousseau & Wassila Ouerdane & Marc Pirlot & Olivier Sobrie, 2023. "Multiple criteria sorting models and methods—Part I: survey of the literature," 4OR, Springer, vol. 21(1), pages 1-46, March.
    21. Bonifacio Llamazares, 2019. "An Analysis of Winsorized Weighted Means," Group Decision and Negotiation, Springer, vol. 28(5), pages 907-933, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:mathme:v:91:y:2020:i:1:d:10.1007_s00186-019-00675-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.