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A characterization of the 2-additive Choquet integral through cardinal information

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Listed:
  • Brice Mayag

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales) - THALES [France] - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique)

  • Michel Grabisch

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

  • Christophe Labreuche

    (Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales) - THALES [France] - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique)

Abstract

In the context of multiple criteria decision analysis, we present the necessary and sufficient conditions to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones.
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Suggested Citation

  • 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.
    • Handle: RePEc:hal:cesptp:halshs-00445132
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    References listed on IDEAS

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    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. 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.
    3. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, January.
    4. 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.
    5. 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.
    6. Gajdos, Thibault, 2002. "Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities," Journal of Economic Theory, Elsevier, vol. 106(1), pages 190-200, September.
    7. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    8. 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.
    9. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    10. Miranda, P. & Grabisch, M. & Gil, P., 2005. "Axiomatic structure of k-additive capacities," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 153-178, March.
    11. Hsee, Christopher K., 1996. "The Evaluability Hypothesis: An Explanation for Preference Reversals between Joint and Separate Evaluations of Alternatives," Organizational Behavior and Human Decision Processes, Elsevier, vol. 67(3), pages 247-257, September.
    12. Alain Chateauneuf & Robert Kast & André Lapied, 2001. "Conditioning Capacities and Choquet Integrals: The Role of Comonotony," Theory and Decision, Springer, vol. 51(2), pages 367-386, December.
    13. Bana e Costa, Carlos A. & Corrêa, Émerson C. & De Corte, Jean-Marie & Vansnick, Jean-Claude, 2002. "Facilitating bid evaluation in public call for tenders: a socio-technical approach," Omega, Elsevier, vol. 30(3), pages 227-242, June.
    14. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
    15. Cliville, Vincent & Berrah, Lamia & Mauris, Gilles, 2007. "Quantitative expression and aggregation of performance measurements based on the MACBETH multi-criteria method," International Journal of Production Economics, Elsevier, vol. 105(1), pages 171-189, January.
    16. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    17. Mousset, Céline, 2009. "Families of relations modelling preferences under incomplete information," European Journal of Operational Research, Elsevier, vol. 192(2), pages 538-548, January.
    18. Michel Grabisch & Jacques Duchene & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Positions," Post-Print halshs-00273179, HAL.
    19. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
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    Cited by:

    1. Beliakov, Gleb, 2022. "Knapsack problems with dependencies through non-additive measures and Choquet integral," European Journal of Operational Research, Elsevier, vol. 301(1), pages 277-286.
    2. Li, Jianping & Yao, Xiaoyang & Sun, Xiaolei & Wu, Dengsheng, 2018. "Determining the fuzzy measures in multiple criteria decision aiding from the tolerance perspective," European Journal of Operational Research, Elsevier, vol. 264(2), pages 428-439.
    3. 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.
    4. 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.
    5. Kadaifci, Cigdem & Asan, Umut & Bozdag, Erhan, 2020. "A new 2-additive Choquet integral based approach to qualitative cross-impact analysis considering interaction effects," Technological Forecasting and Social Change, Elsevier, vol. 158(C).
    6. 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.

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    Keywords

    Choquet integral; 2-additive capacity;

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