IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v244y2016i2d10.1007_s10479-012-1166-6.html
   My bibliography  Save this article

Choquet integral with respect to a symmetric fuzzy measure of a function on the real line

Author

Listed:
  • Yasuo Narukawa

    (Toho Gakuen
    Tokyo Institute of Technology)

  • Vicenç Torra

    (IIIA—CSIC)

  • Michio Sugeno

    (European Centre for Soft Computing)

Abstract

Some results about the calculation of the Choquet integral of a monotone function are presented. The construction of monotone functions from non-monotone ones that lead to the same Choquet integral is studied. The paper is completed with the application of these results to the continuous WOWA operator, as well as with some differential equations also applied to the determination of the weight in this operator.

Suggested Citation

  • Yasuo Narukawa & Vicenç Torra & Michio Sugeno, 2016. "Choquet integral with respect to a symmetric fuzzy measure of a function on the real line," Annals of Operations Research, Springer, vol. 244(2), pages 571-581, September.
  • Handle: RePEc:spr:annopr:v:244:y:2016:i:2:d:10.1007_s10479-012-1166-6
    DOI: 10.1007/s10479-012-1166-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-012-1166-6
    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/s10479-012-1166-6?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. Ulrich Faigle & Michel Grabisch, 2011. "A Discrete Choquet Integral for Ordered Systems," Post-Print halshs-00563926, HAL.
    2. Itzhak Gilboa & David Schmeidler, 1992. "Additive Representation of Non-Additive Measures and the Choquet Integral," Discussion Papers 985, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. 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.
    4. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    5. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
    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. Torra, Vicenç, 2023. "The transport problem for non-additive measures," European Journal of Operational Research, Elsevier, vol. 311(2), pages 679-689.
    2. LeSheng Jin & Radko Mesiar & Martin Kalina & Ronald R. Yager, 2020. "Canonical form of ordered weighted averaging operators," Annals of Operations Research, Springer, vol. 295(2), pages 605-631, December.
    3. Hamzeh Agahi, 2020. "On fractional continuous weighted OWA (FCWOWA) operator with applications," Annals of Operations Research, Springer, vol. 287(1), pages 1-10, April.
    4. Negi, Shekhar Singh & Torra, Vicenç, 2022. "Δ-Choquet integral on time scales with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(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, 2015. "Fuzzy Measures and Integrals: Recent Developments," Post-Print hal-01302377, HAL.
    2. Luca Anzilli & Silvio Giove, 2020. "Multi-criteria and medical diagnosis for application to health insurance systems: a general approach through non-additive measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 43(2), pages 559-582, December.
    3. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2009. "A characterization of the 2-additive Choquet integral through cardinal information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445132, HAL.
    4. Peter Reichert & Klemens Niederberger & Peter Rey & Urs Helg & Susanne Haertel-Borer, 2019. "The need for unconventional value aggregation techniques: experiences from eliciting stakeholder preferences in environmental management," EURO Journal on Decision Processes, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 197-219, November.
    5. Bonifacio Llamazares, 2019. "An Analysis of Winsorized Weighted Means," Group Decision and Negotiation, Springer, vol. 28(5), pages 907-933, October.
    6. Corrente, Salvatore & Greco, Salvatore & Ishizaka, Alessio, 2016. "Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression," Omega, Elsevier, vol. 61(C), pages 2-18.
    7. Mikhail Timonin, 2016. "Choquet integral in decision analysis - lessons from the axiomatization," Papers 1611.09926, arXiv.org.
    8. 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.
    9. Alessio Bonetti & Silvia Bortot & Mario Fedrizzi & Silvio Giove & Ricardo Alberto Marques Pereira & Andrea Molinari, 2011. "Modelling group processes and effort estimation in Project Management using the Choquet integral: an MCDM approach," DISA Working Papers 2011/12, Department of Computer and Management Sciences, University of Trento, Italy, revised Sep 2011.
    10. Labreuche, Christophe & Grabisch, Michel, 2018. "Using multiple reference levels in Multi-Criteria Decision aid: The Generalized-Additive Independence model and the Choquet integral approaches," European Journal of Operational Research, Elsevier, vol. 267(2), pages 598-611.
    11. Jian-Zhang Wu & Yi-Ping Zhou & Li Huang & Jun-Jie Dong, 2019. "Multicriteria Correlation Preference Information (MCCPI)-Based Ordinary Capacity Identification Method," Mathematics, MDPI, vol. 7(3), pages 1-13, March.
    12. Silvia Bortot & Mario Fedrizzi & Silvio Giove, 2011. "Modelling fraud detection by attack trees and Choquet integral," DISA Working Papers 2011/09, Department of Computer and Management Sciences, University of Trento, Italy, revised 31 Aug 2011.
    13. GRABISCH, Michel & LABREUCHE, Christophe & RIDAOUI, Mustapha, 2019. "On importance indices in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 277(1), pages 269-283.
    14. Silvia Bortot & Ricardo Alberto Marques Pereira, 2011. "Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process," DISA Working Papers 2011/06, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.
    15. Francesco Tajani & Maria Rosaria Guarini & Francesco Sica & Rossana Ranieri & Debora Anelli, 2022. "Multi-Criteria Analysis and Sustainable Accounting. Defining Indices of Sustainability under Choquet’s Integral," Sustainability, MDPI, vol. 14(5), pages 1-15, February.
    16. Li Huang & Jian-Zhang Wu & Rui-Jie Xi, 2020. "Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    17. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
    18. Zhang, Ling & Zhang, Luping & Zhou, Peng & Zhou, Dequn, 2015. "A non-additive multiple criteria analysis method for evaluation of airline service quality," Journal of Air Transport Management, Elsevier, vol. 47(C), pages 154-161.
    19. Kolesárová, Anna & Li, Jun & Mesiar, Radko, 2018. "k-additive aggregation functions and their characterization," European Journal of Operational Research, Elsevier, vol. 265(3), pages 985-992.
    20. Yaarit Even & Ehud Lehrer, 2014. "Decomposition-integral: unifying Choquet and the concave integrals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 33-58, May.

    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:annopr:v:244:y:2016:i:2:d:10.1007_s10479-012-1166-6. 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.