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Rectification of Preferences in a Fuzzy Environment.

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Abstract
In this paper we consider a complete fuzzy preference structure, defined by means of a constructive approach associated to the necessary learning process in a decision making problem. Preference relations are successively assigned over a given set of alternatives with the possibility of revision and rectification, subject to a certain set of beliefs which sustain the construction of different viewpoints. Measures of information are then considered in this process for a formal identification of uncertainty due to ignorance, a concept that is closely related to ambiguity as defined by Fishburn (1993). Finally, a coherence criterion is proposed in order to study the importance of preferences, in such a way that an indirect and comparative analysis between them is needed so outcomes may be coherently organized.
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13th International Conference, IPMU 2010, Dortmund, Germany, June 28–July 2, 2010. Proceedings, Part I
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Amo, A., Montero, J., Biging, G., Cutello, V.: Fuzzy classification systems. European Journal of Operational Research 156, 459–507 (2004) Atanassov, K.: Intuitionistic Fuzzy Sets. Theory and Applications. Physica-Verlag, New York (1999) Bouyssou, D., Marchant, T., Pirlot, M., Tsoukiàs, A., Vincke, P.: Evaluation and Decision Models with Multiple Criteria, vol. 86. Springer, Heidelberg (2006) Bustince, H., Fernández, J., Mesiar, R., Montero, J.: Overlap function. Non Linear Analysis 72, 1488–1499 (2010) Cubillo, S., Bellido, S.: A first approximation to Ng-coherence measures. In: Proceedings EUSFLAT 2003, pp. 709–713 (2003) Dubois, D., Prade, H.: Formal representations of uncertainty. In: Bouyssou, D., Dubois, D., Pirlot, M., Prade, H. (eds.) Decision-Making Process. ISTE, London (2009) Ellsberg, D.: Risk ambiguity and the savage axioms. Quarterly Journal of Economics 75, 643–69 (1961) Fishburn, P.: The axioms and algebra of ambiguity. Theory and Decision 34, 119–137 (1993) Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994) Fox, C., Tversky, A.: Ambiguity aversion and comparative ignorance. The Quarterly Journal of Economics 110, 585–603 (1995) Franco de los Ríos, C., Montero, J.: On the use of coherence measures for fuzzy preference relations. In: Eurofuse Workshop 2009, pp. 15–19 (2009) González-Pachón, J., Gómez, D., Montero, J., Yáñez, J.: Soft dimension theory. Fuzzy Sets and Systems 137, 137–149 (2003) Junker, U.: Preferences in an open world. In: First International Conference, ADT 2009,pp. 215–224 (2009) Keynes, J.: A Treatise on Probability. MacMillan, London (1963) Knight, F.: Risk, Uncertainty, and Profit. University of Chicago Press, Chicago (1971) Montero, J., Gómez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy ets and Systems 158, 2429–2442 (2007) Montero, J., Tejada, J., Cutello, C.: A general model for deriving preference structures from data. European Journal of Operational Research 98, 98–110 (1997) Nebel, B.: A knowledge level analysis of belief revision. In: Proceedings of the 1st International Conference on Principles of Knowledge Representation and Reasoning, pp. 301–311 (1989) Öztürk, M., Tsoukiàs, A.: Modelling uncertain positive and negative reasons in decision aiding. Decision Support Systems 43, 1512–1526 (2007) Sancho-Royo, A., Verdegay, J.: Coherence measures on finite fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 8, 641–663 (2000) Sancho-Royo, A., Verdegay, J.: Fuzzy coherence measures. International Journal of Intelligent Systems 20, 1–11 (2005) Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118, 467–477 (2001) Trillas, E.: On the use of words and fuzzy sets.Information Sciences 176, 1463–1487 (2006) Yager, R.: On a measure of ambiguity. International Journal of Intelligent Systems 10, 1001–1019 (1995) Zadeh, L.: Fuzzy sets. Information and Control 8, 338–353 (1965) Zadeh, L.: The concept of a linguistic variable and its application to aproximate reasoning. Information Sciences 8, 199–249 (1975) Zadeh, L.: Fuzzy sets and information granularity. In: Adavances in Fuzzy Set Theory and applications, pp. 3–18. North-Holland, Amsterdam (1979)