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Generalized Choquet-like aggregation functions for handling bipolar scales

Listed author(s):
  • Labreuche, Christophe
  • Grabisch, Michel

We are interested in modeling interaction between criteria in Multi-Criteria Decision Making when underlying scales are bipolar. Interacting phenomena involving behavioral bias between attractive and repulsive values are in particular considered here. We show in an example that both the Choquet integral and the Cumulative Prospect Theory (CPT) model fail to represent these interacting phenomena. Axioms that enable the construction of the preferences of the decision maker over each attribute, and the representation of his preferences about aggregation of criteria are introduced and justified. We show there is a unique aggregation operator that fits with these axioms. It is based on the notion of {\em bi-capacity} and generalizes both the Choquet integral and the CPT model.

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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 172 (2006)
Issue (Month): 3 (August)
Pages: 931-955

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Handle: RePEc:eee:ejores:v:172:y:2006:i:3:p:931-955
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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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. 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.
  3. 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.
  4. Michel Grabisch & Christophe Labreuche, 2002. "The symmetric and asymmetric Choquet integrals on finite spaces for decision making," Statistical Papers, Springer, vol. 43(1), pages 37-52, January.
  5. 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.
  6. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
  7. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
  8. 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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