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

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  • Michel Grabisch

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

  • Christophe Labreuche

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

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," Post-Print halshs-00267932, HAL.
  • Handle: RePEc:hal:journl:halshs-00267932
    DOI: 10.1007/s10288-007-0064-2
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00267932
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    File URL: https://halshs.archives-ouvertes.fr/halshs-00267932/document
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    References listed on IDEAS

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    7. Marichal, Jean-Luc, 2007. "k-intolerant capacities and Choquet integrals," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1453-1468, March.
    8. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
    9. 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.
    10. 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.
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    13. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
    14. Dieter Denneberg & Michel Grabisch, 2004. "Measure and integral with purely ordinal scales," Post-Print hal-00272078, HAL.
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    Citations

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    Cited by:

    1. Mikhail Timonin, 2015. "Axiomatization of the Choquet integral for 2-dimensional heterogeneous product sets," Papers 1507.04167, arXiv.org, revised Mar 2016.
    2. 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.
    3. Mikhail Timonin, 2012. "Maximization of the Choquet integral over a convex set and its application to resource allocation problems," Annals of Operations Research, Springer, vol. 196(1), pages 543-579, July.
    4. Denis Bouyssou & Silvano Martello & Frank Plastria, 2010. "Eleven surveys in operations research: II," Annals of Operations Research, Springer, vol. 175(1), pages 3-8, March.
    5. Silvia Bortot & Ricardo Alberto Marques Pereira & Thuy H. Nguyen, 2015. "Welfare functions and inequality indices in the binomial decomposition of OWA functions," DEM Discussion Papers 2015/08, Department of Economics and Management.
    6. Leo Liberti & Thierry Marchant & Silvano Martello, 2013. "Eleven surveys in operations research: III," Annals of Operations Research, Springer, vol. 204(1), pages 3-9, April.
    7. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    8. Michel Grabisch & Christophe Labreuche, 2019. "Interpretation of multicriteria decision making models with interacting criteria," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381243, HAL.
    9. Leo Liberti & Thierry Marchant & Silvano Martello, 2016. "Twelve surveys in operations research," Annals of Operations Research, Springer, vol. 240(1), pages 3-11, May.
    10. Ferreira, João J.M. & Jalali, Marjan S. & Ferreira, Fernando A.F., 2018. "Enhancing the decision-making virtuous cycle of ethical banking practices using the Choquet integral," Journal of Business Research, Elsevier, vol. 88(C), pages 492-497.
    11. Yves Crama & Michel Grabisch & Silvano Martello, 2018. "Surveys in operations research," Annals of Operations Research, Springer, vol. 271(1), pages 3-10, December.
    12. Mikhail Timonin, 2016. "Choquet integral in decision analysis - lessons from the axiomatization," Papers 1611.09926, arXiv.org.
    13. 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.
    14. 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.
    15. Michel Grabisch & Christophe Labreuche, 2019. "Interpretation of multicriteria decision making models with interacting criteria," Post-Print halshs-02381243, HAL.
    16. Angilella, Silvia & Corrente, Salvatore & Greco, Salvatore, 2015. "Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem," European Journal of Operational Research, Elsevier, vol. 240(1), pages 172-182.
    17. Ulrich Faigle & Michel Grabisch, 2011. "A Discrete Choquet Integral for Ordered Systems," Post-Print halshs-00563926, HAL.
    18. Jun-Jie Dong & Jian-Zhang Wu & Endre Pap & Aniko Szakal, 2017. "A Choquet Capacity and Integral Based Method to Identify the Overall Importance of Engineering Characteristics in Quality Function Deployment," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(4), pages 297-314.
    19. Zhang, Ling & Zhou, Peng & Newton, Sidney & Fang, Jian-xin & Zhou, De-qun & Zhang, Lu-ping, 2015. "Evaluating clean energy alternatives for Jiangsu, China: An improved multi-criteria decision making method," Energy, Elsevier, vol. 90(P1), pages 953-964.
    20. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Post-Print halshs-00496558, HAL.
    21. Mikhail Timonin, 2016. "Conjoint axiomatization of the Choquet integral for heterogeneous product sets," Papers 1603.08142, arXiv.org.
    22. F. Beaudouin, 2015. "Implementing a Multiple Criteria Model to Debate About Nuclear Power Plants Safety Choices," Group Decision and Negotiation, Springer, vol. 24(6), pages 1035-1063, November.

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