Abstract
Main decision-making problems can be described into choice, ranking or sorting of a set of alternatives or solutions. The principle of Electre TRI (ET) method is to sort alternatives ai according to criteria g j into categories C h whose lower and upper limits are respectively b h and b h + 1. The sorting procedure is based on the evaluations of outranking relations based firstly on calculation of partial concordance and discordance indexes and secondly on global concordance and credibility indexes. In this paper, we propose to replace the calculation of the original concordance and discordance indexes of ET method by a more effective sigmoidal model. Such model is part of a new Belief Function ET (BF-ET) method under development and allows a comprehensive, elegant and continuous mathematical representation of degree of concordance, discordance and the uncertainty level which is not directly taken into account explicitly in the classical Electre Tri.
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References
Dezert, J., Smarandache, F.: Proportional Conflict Redistribution Rules for Information Fusion. In: [8], vol. 2, pp. 3–68 (2006)
Dezert, J., Smarandache, F.: An introduction to DSmT. In: [8], vol. 3, pp. 3–73 (2009)
Dezert, J., Smarandache, F., Tacnet, J.-M., Batton-Hubert, M.: Multi-criteria decision making based on DSmT/AHP. In: International Workshop on Belief Functions, Brest, France (April 2010)
Dezert, J., Liu, Z., Mercier, G.: Edge Detection in Color Images Based on DSmT. In: Proceedings of Fusion 2011, Chicago, USA (July 2011)
Figueira, J., Mousseau, V., Roy, B.: ELECTRE methods. In: Multiple Criteria Decision Analysis: State of Art Surveys, ch. 4. Springer Science+Business Media Inc. (2005)
Mousseau, V., Slowinski, R., Zielniewicz, P.: Electre tri 2.0a - methological guide and user’s manual - document no 111. In: Cahier et Documents du Lamsade, Lamsade, Université Paris-Dauphine, Paris (1999)
Shafer, G.: A mathematical theory of evidence. Princeton University Press (1976)
Smarandache, F., Dezert, J.: Advances and applications of DSmT for information fusion (Collected works), vol. 1-3. American Research Press (2004-2009), http://www.gallup.unm.edu/~smarandache/DSmT.htm
Smarandache, F., Dezert, J., Tacnet, J.-M.: Fusion of sources of evidence with different importances and reliabilities. In: Proc. of Fusion 2010 Conf., Edinburgh, UK (July 2010)
Tacnet, J.-M., Dezert, J.: Cautious OWA and Evidential Reasoning for Decision Making under Uncertainty. In: Proceedings of Fusion 2011, Chicago, USA (July 2011)
Tacnet, J.-M., Batton-Hubert, M., Dezert, J.: A two-step fusion process for multi-criteria decision applied to natural hazards in mountains. In: Proceedings of International Workshop on the Theory of Belief Functions, Belief 2010, Brest (France), April 1-2 (2010)
Tervonen, T., Figueira, J.R., Lahdelma, R., Dias, J.A., Salminen, P.: A stochastic method for robustness analysis in sorting problems. European Journal of Operational Research 192, 236–242 (2009)
Yu, W.: Aide multicritère à la décision dans le cadre de la problématique du tri: Concepts, méthodes et applications. Ph.D Thesis, University Paris-Dauphine, France (1992)
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Dezert, J., Tacnet, JM. (2012). Sigmoidal Model for Belief Function-Based Electre Tri Method. In: Denoeux, T., Masson, MH. (eds) Belief Functions: Theory and Applications. Advances in Intelligent and Soft Computing, vol 164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29461-7_47
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DOI: https://doi.org/10.1007/978-3-642-29461-7_47
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