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A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid

Author

Listed:
  • Michel Grabisch

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

  • Christophe Labreuche

    (Thales Research and Technology [Palaiseau] - THALES [France])

Abstract

The main advances regarding the use of the Choquet and Sugeno integrals in multi-criteria decision aid over the last decade are reviewed. They concern mainly a bipolar extension of both the Choquet integral and the Sugeno integral, interesting particular submodels, new learning techniques, a better interpretation of the models and a better use of the Choquet integral in multi-criteria decision aid. Parallel to these theoretical works, the Choquet integral has been applied to many new fields, and several softwares and libraries dedicated to this model have been developed.

Suggested Citation

  • Michel Grabisch & Christophe Labreuche, 2008. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00267932, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00267932
    DOI: 10.1007/s10288-007-0064-2
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00267932
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    References listed on IDEAS

    as
    1. 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.
    2. Christophe Labreuche & Michel Grabisch, 2008. "A value for bi-cooperative games," Post-Print halshs-00308738, HAL.
    3. 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.
    4. 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.
    5. Michel Grabisch & Jean-Luc Marichal & Marc Roubens, 2000. "Equivalent Representations of Set Functions," Mathematics of Operations Research, INFORMS, vol. 25(2), pages 157-178, May.
    6. 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.
    7. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    8. 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.
    9. Agnès Rico & Michel Grabisch & Christophe Labreuche & Alain Chateauneuf, 2005. "Preference modelling on totally ordered sets by the Sugeno integral," Post-Print hal-00268984, HAL.
    10. 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.
    11. Michel Grabisch, 2003. "The Symmetric Sugeno Integral," Post-Print hal-00272084, HAL.
    12. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
    13. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    14. Christophe Labreuche & M. Grabisch, 2007. "The representation of conditional relative importance between criteria," Annals of Operations Research, Springer, vol. 154(1), pages 93-122, October.
    15. 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.
    16. Marichal, Jean-Luc, 2007. "k-intolerant capacities and Choquet integrals," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1453-1468, March.
    17. Christophe Labreuche & Michel Grabisch, 2006. "Definition of an importance index for bi-capacities in MCDA," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00186895, HAL.
    18. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
    19. repec:dau:papers:123456789/4795 is not listed on IDEAS
    20. Fujimoto, Katsushige & Kojadinovic, Ivan & Marichal, Jean-Luc, 2006. "Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices," Games and Economic Behavior, Elsevier, vol. 55(1), pages 72-99, April.
    21. Marichal, Jean-Luc & Roubens, Marc, 2000. "Determination of weights of interacting criteria from a reference set," European Journal of Operational Research, Elsevier, vol. 124(3), pages 641-650, August.
    22. 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.
    23. Liginlal, Divakaran & Ow, Terence T., 2005. "On policy capturing with fuzzy measures," European Journal of Operational Research, Elsevier, vol. 167(2), pages 461-474, December.
    24. 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.
    25. Michel Grabisch & Éric Raufaste, 2008. "An empirical study of statistical properties of Choquet and Sugeno integrals," Post-Print halshs-00445168, HAL.
    26. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
    27. 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.
    28. Michel Grabisch, 2004. "The Möbius transform on symmetric ordered structures and its application to capacities on finite sets," Post-Print hal-00188158, HAL.
    29. Dieter Denneberg & Michel Grabisch, 2004. "Measure and integral with purely ordinal scales," Post-Print hal-00272078, HAL.
    30. Jesús Mario Bilbao & Julio R. Fernández & Nieves Jiménez & Jorge Jesús López, 2004. "The Shapley value for bicooperative games," Economic Working Papers at Centro de Estudios Andaluces E2004/56, Centro de Estudios Andaluces.
    31. 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.
    32. Kojadinovic, Ivan, 2007. "Minimum variance capacity identification," European Journal of Operational Research, Elsevier, vol. 177(1), pages 498-514, February.
    33. Michel Grabisch & Jacques Duchene & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Positions," Post-Print halshs-00273179, HAL.
    34. Berrah, L. & Mauris, G. & Montmain, J., 2008. "Monitoring the improvement of an overall industrial performance based on a Choquet integral aggregation," Omega, Elsevier, vol. 36(3), pages 340-351, June.
    35. Marichal, Jean-Luc, 2004. "Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral," European Journal of Operational Research, Elsevier, vol. 155(3), pages 771-791, June.
    36. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
    Full references (including those not matched with items on IDEAS)

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