IDEAS home Printed from https://ideas.repec.org/h/spr/isochp/978-1-4939-3094-4_14.html
   My bibliography  Save this book chapter

Fuzzy Measures and Integrals in MCDA

In: Multiple Criteria Decision Analysis

Author

Listed:
  • Michel Grabisch

    (Université Paris I - Panthéon-Sorbonne)

  • Christophe Labreuche

    (Thales Research & Technology)

Abstract

This chapter aims at a unified presentation of various methods of MCDA based on fuzzy measures (capacity) and fuzzy integrals, essentially the Choquet and Sugeno integral. A first section sets the position of the problem of multicriteria decision making, and describes the various possible scales of measurement (cardinal unipolar and bipolar, and ordinal). Then a whole section is devoted to each case in detail: after introducing necessary concepts, the methodology is described, and the problem of the practical identification of fuzzy measures is given. The important concept of interaction between criteria, central in this chapter, is explained in detail. It is shown how it leads to k-additive fuzzy measures. The case of bipolar scales leads to the general model based on bi-capacities, encompassing usual models based on capacities. A general definition of interaction for bipolar scales is introduced. The case of ordinal scales leads to the use of Sugeno integral, and its symmetrized version when one considers symmetric ordinal scales. A practical methodology for the identification of fuzzy measures in this context is given.

Suggested Citation

  • Michel Grabisch & Christophe Labreuche, 2016. "Fuzzy Measures and Integrals in MCDA," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 553-603, Springer.
    • Handle: RePEc:spr:isochp:978-1-4939-3094-4_14
    DOI: 10.1007/978-1-4939-3094-4_14
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2019. "Interaction indices for multichoice games," Documents de travail du Centre d'Economie de la Sorbonne 19019, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Grabisch, Michel & Labreuche, Christophe & Vansnick, Jean-Claude, 2003. "On the extension of pseudo-Boolean functions for the aggregation of interacting criteria," European Journal of Operational Research, Elsevier, vol. 148(1), pages 28-47, July.
    3. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    4. Michel Grabisch & Christophe Labreuche, 2002. "The symmetric and asymmetric Choquet integrals on finite spaces for decision making," Statistical Papers, Springer, vol. 43(1), pages 37-52, January.
    5. Pedro Miranda & Michel Grabisch, 2004. "p-symmetric bi-capacities," Post-Print halshs-00188173, HAL.
    6. Michel Grabisch, 2009. "Subjective Evaluation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00671303, HAL.
    7. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    8. Dubois, Didier & Prade, Henri & Sabbadin, Regis, 2001. "Decision-theoretic foundations of qualitative possibility theory," European Journal of Operational Research, Elsevier, vol. 128(3), pages 459-478, February.
    9. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
    10. Michel Grabisch, 2003. "The Symmetric Sugeno Integral," Post-Print hal-00272084, HAL.
    11. Dieter Denneberg & Michel Grabisch, 2004. "Measure and integral with purely ordinal scales," Post-Print hal-00272078, HAL.
    12. MoshÊ Machover & Dan S. Felsenthal, 1997. "Ternary Voting Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 335-351.
    13. Michel Grabisch & Jacques Duchene & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Positions," Post-Print halshs-00273179, HAL.
    14. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
    Full references (including those not matched with items on IDEAS)

    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 & 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.
    2. 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.
    3. 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.
    4. 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.
    5. Michel Grabisch, 2006. "Evaluation subjective," Post-Print halshs-00179068, HAL.
    6. Kojadinovic, Ivan, 2007. "A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral," European Journal of Operational Research, Elsevier, vol. 179(2), pages 498-517, June.
    7. Labreuche, Christophe & Grabisch, Michel, 2006. "Generalized Choquet-like aggregation functions for handling bipolar scales," European Journal of Operational Research, Elsevier, vol. 172(3), pages 931-955, August.
    8. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Post-Print hal-01302377, HAL.
    9. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    10. Chateauneuf, A. & Grabisch, M. & Rico, A., 2008. "Modeling attitudes toward uncertainty through the use of the Sugeno integral," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1084-1099, December.
    11. Michel Grabisch & Salvatore Greco & Marc Pirlot, 2008. "Bipolar and bivariate models in multi-criteria decision analysis: descriptive and constructive approaches," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00340374, HAL.
    12. Kojadinovic, Ivan & Marichal, Jean-Luc, 2007. "Entropy of bi-capacities," European Journal of Operational Research, Elsevier, vol. 178(1), pages 168-184, April.
    13. Miranda, P. & Grabisch, M. & Gil, P., 2005. "Axiomatic structure of k-additive capacities," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 153-178, March.
    14. Michel Grabisch, 2003. "The Symmetric Sugeno Integral," Post-Print hal-00272084, HAL.
    15. Michel Grabisch, 2006. "Aggregation on bipolar scales," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00187155, HAL.
    16. Grabisch, Michel, 2006. "Representation of preferences over a finite scale by a mean operator," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 131-151, September.
    17. Grabisch, Michel & Rusinowska, Agnieszka, 2011. "Influence functions, followers and command games," Games and Economic Behavior, Elsevier, vol. 72(1), pages 123-138, May.
    18. Grabisch, Michel & Labreuche, Christophe & Vansnick, Jean-Claude, 2003. "On the extension of pseudo-Boolean functions for the aggregation of interacting criteria," European Journal of Operational Research, Elsevier, vol. 148(1), pages 28-47, July.
    19. Michel Grabisch & Bernard de Baets & Janos Fodor, 2004. "The quest for rings on bipolar scales," Post-Print hal-00271217, HAL.
    20. Marichal, Jean-Luc, 2007. "k-intolerant capacities and Choquet integrals," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1453-1468, March.

    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:isochp:978-1-4939-3094-4_14. 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.