Abstract
In the context of Multiple Criteria Decision aiding (MCDA), we present necessary conditions to obtain a representation of a cardinal information by a Choquet integral w.r.t a 2-additive capacity. A cardinal information is a preferential information provided by a Decision Maker (DM) containing a strict preference, a quaternary and indifference relations. Our work is focused on the representation of a cardinal information by a particular Choquet integral defined by a 2-additive capacity. Used as an aggregation function, it arises as a generalization of the arithmetic mean, taking into account the interaction between two criteria. Then, it is a good compromise between simple models like arithmetic mean and complex models like general Choquet integral. We consider also the set of fictitious alternatives called binary alternatives or binary actions from which the Choquet integral w.r.t a 2-additive capacity can be entirely specified. The proposed MOPIC (MOnotonicity of Preferential Information for Cardinal) conditions can be viewed as an alternative to balanced cyclones which are complex necessary and sufficient conditions, used in the characterization of a 2-additive Choquet integral through a cardinal information.
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References
Bana e Costa, C.A., Correa, E.C., De Corte, J.-M., Vansnick, J.-C.: Facilitating bid evaluation in public call for tenders: a socio-technical approach. Omega 30, 227–242 (2002)
Bana e Costa, C.A., De Corte, J.-M., Vansnick, J.-C.: Macbeth. Int. J. Inf. Technol. Decis. Making 11(2), 359–387 (2012)
Chateauneuf, A., Jaffray, J.Y.: Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion. Math. Soc. Sci. 17, 263–283 (1989)
Clivillé, V., Berrah, L., Mauris, G.: Quantitative expression and aggregation of performance measurements based on the MACBETH multi-criteria method. Int. J. Prod. Econ. 105, 171–189 (2007)
Grabisch, M.: \(k\)-order additive discrete fuzzy measures and their representation. Fuzzy Sets Syst. 92, 167–189 (1997)
Grabisch, M., Labreuche, C.: Fuzzy measures and integrals in MCDA. In: Figueira, J., Greco, S., Ehrgott, M. (eds.) Multiple Criteria Decision Analysis: State of the Art Surveys, vol. 78, pp. 565–608. Springer, New York (2005)
Grabisch, M., Labreuche, Ch.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. 4OR 6, 1–44 (2008)
Marchant, T.: Towards a theory of MCDM: stepping away from social choice theory. Math. Soc. Sci. 45(3), 343–363 (2003)
Mayag, B., Grabisch, M., Labreuche, C.: An interactive algorithm to deal with inconsistencies in the representation of cardinal information. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds.) IPMU 2010. CCIS, vol. 80, pp. 148–157. Springer, Heidelberg (2010)
Mayag, B., Grabisch, M., Labreuche, Ch.: A characterization of the 2-additive Choquet integral through cardinal information. Fuzzy Sets Syst. 184, 84–105 (2011)
Mayag, B., Grabisch, M., Labreuche, Ch.: A representation of preferences by the Choquet integral with respect to a 2-additive capacity. Theory Decis. 71, 297–324 (2011)
Simon, H.: Rational choice and the structure of the environment. Psychol. Rev. 63(2), 129–138 (1956)
Slovic, P., Finucane, M., Peters, E., MacGregor, D.G.: The affect heuristic. In: Gilovitch, T., Griffin, D., Kahneman, D. (eds.) Heuristics and Biases: The Psychology of Intuitive Judgment, pp. 397–420. Cambridge University Press (2002)
Tversky, A., Kahneman, D.: Advances in prospect theory: cumulative representation of uncertainty. J. Risk Uncertainty 5, 297–323 (1992)
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Mayag, B. (2015). MOPIC Properties in the Representation of Preferences by a 2-Additive Choquet Integral. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_14
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DOI: https://doi.org/10.1007/978-3-319-23114-3_14
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