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A representation of preferences by the Choquet integral with respect to a 2-additive capacity

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  • Brice Mayag
  • Michel Grabisch
  • Christophe Labreuche
Abstract
In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.
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  • 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.
    • Handle: RePEc:kap:theord:v:71:y:2011:i:3:p:297-324
    DOI: 10.1007/s11238-010-9198-3
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    1. Bana e Costa, Carlos A. & Nunes da Silva, Fernando & Vansnick, Jean-Claude, 2001. "Conflict dissolution in the public sector: A case-study," European Journal of Operational Research, Elsevier, vol. 130(2), pages 388-401, April.
    2. Marchant, Thierry, 2003. "Towards a theory of MCDM: stepping away from social choice theory," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 343-363, July.
    3. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2008. "A characterization of the 2-additive Choquet integral," Post-Print halshs-00644232, HAL.
    4. 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.
    5. 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.
    6. Miranda, P. & Grabisch, M. & Gil, P., 2005. "Axiomatic structure of k-additive capacities," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 153-178, March.
    7. 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.
    8. 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.
    9. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    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. 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.
    12. 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.
    13. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    14. Michel Grabisch & Jacques Duchene & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Positions," Post-Print halshs-00273179, HAL.
    15. 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.
    16. 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.
    17. 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.
    18. Jaffray, Jean-Yves & Wakker, Peter, 1993. "Decision Making with Belief Functions: Compatibility and Incompatibility with the Sure-Thing Principle," Journal of Risk and Uncertainty, Springer, vol. 7(3), pages 255-271, December.
    19. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
    20. 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.
    21. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
    22. 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.
    23. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
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    2. 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.
    3. Brunelli, Matteo & Corrente, Salvatore, 2024. "Modeling criteria and project interactions in portfolio decision analysis with the Choquet integral," Omega, Elsevier, vol. 126(C).
    4. Paul Alain Kaldjob Kaldjob & Brice Mayag & Denis Bouyssou, 2022. "On the robustness of the sign of nonadditivity index in a Choquet integral model," Post-Print hal-03904424, HAL.
    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. Axel C. Mühlbacher & Anika Kaczynski, 2016. "Making Good Decisions in Healthcare with Multi-Criteria Decision Analysis: The Use, Current Research and Future Development of MCDA," Applied Health Economics and Health Policy, Springer, vol. 14(1), pages 29-40, February.
    7. Paul Alain Kaldjob Kaldjob & Brice Mayag & Denis Bouyssou, 2023. "On the interpretation of the interaction index between criteria in a Choquet integral model," Post-Print hal-03766372, HAL.
    8. 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.
    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. Serena Doria, 2019. "Preference orderings represented by coherent upper and lower conditional previsions," Theory and Decision, Springer, vol. 87(2), pages 233-252, September.
    11. 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).
    12. Sébastien Courtin & Rodrigue Tido Takeng & Frédéric Chantreuil, 2020. "Decomposition of interaction indices: alternative interpretations of cardinal-probabilistic interaction indices ," Working Papers hal-02952516, HAL.
    13. 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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