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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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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00625706.

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Date of creation: 2011
Date of revision:
Publication status: Published, Theory and Decision, 2011, 71, 3, 297-324
Handle: RePEc:hal:cesptp:halshs-00625706

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00625706
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Related research

Keywords: multicriteria decision making; Choquet integral; 2-additive capacity; MACBETH;

Other versions of this item:

Find related papers by JEL classification:

• C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
• C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
• C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
• D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

This paper has been announced in the following NEP Reports:

• NEP-ALL-2011-10-01 (All new papers)
• NEP-MIC-2011-10-01 (Microeconomics)
• NEP-UPT-2011-10-01 (Utility Models & Prospect Theory)

References

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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. Michel Grabisch & Christophe Labreuche & Jean-Claude Vansnick, 2003. "On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria," Post-Print hal-00272780, HAL.
   
   • 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.
4. 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.
   
   • Michel Grabisch & Christophe Labreuche, 2010. "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-00496558, HAL.
5. Pedro Miranda & Michel Grabisch & Pedro Gil, 2005. "Axiomatic structure of k-additive capacities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00188165, HAL.
   
   • Miranda, P. & Grabisch, M. & Gil, P., 2005. "Axiomatic structure of k-additive capacities," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 153-178, March.
6. 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.
7. 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.
8. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
   
   • David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
9. Alain Chateauneuf & Michel Grabisch & Agnès Rico, 2008. "Modeling attitudes toward uncertainty through the use of the Sugeno integral," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00327700, HAL.
   
   • 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.
10. 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.
11. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
12. Michel Grabisch & Jacques Duchêne & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Positions," Post-Print halshs-00273179, HAL.
13. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
14. 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.
15. 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 255-71, December.
16. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
17. 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.
18. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
19. 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.

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Cited by:

1. 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.
2. 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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