Abstract
Fuzzy (valued) preference relations (FPR) give possibility to take into account the intensity of preference between alternatives. The refinement of crisp (non-valued) preference relations by replacing them with valued preference relations often transforms crisp preference relations with cycles into acyclic FPR. It gives possibility to make decisions in situations when crisp models do not work. Different models of rationality of strict FPR defined by the levels of transitivity or acyclicity of these relations are considered. The choice of the best alternatives based on given strict FPR is defined by a fuzzy choice function (FCF) ordering alternatives in given subset of alternatives. The relationships between rationality of strict FPR and rationality of FCF are studied. Several valued generalizations of crisp group decision-making procedures are proposed. As shown on examples of group decision-making in multiagent systems, taking into account the preference values gives possibility to avoid some problems typical for crisp procedures.
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References
Abaev, L.: Choice of variants in a fuzzy environment: binary relations and fuzzy decomposition. In: Batyrshin, I., Pospelov, D. (eds.) Soft Models in Decision-Making; Special Issue of International Journal of General Systems 30, 53–70 (2001)
Averkin, A., Batyrshin, I., Blishun, A., et al.: Fuzzy Sets in the Models of Control and Artificial Intelligence. Nauka Publ., Moscow (1986) (in Russian)
Bouyssou, D.: Acyclic fuzzy preference and the Orlovsky choice function: a note. Fuzzy Sets and Systems 89, 107–111 (1997)
Danilov, V.I., Sotskov, A.I.: Mechanisms of Group Choice. Nauka Publ., Moscow (1991) (in Russian)
Faratin, P., Van de Walle, B.: Agent Preference Relations: Strict, Equivalent and Incomparables. In: Autonomous Agents and Multi-Agent Systems, pp. 1317–1324. AAAI Press, Italy (2002)
Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)
García-Lapresta, J.L.: A general class of simple majority decision rules based on linguistic opinions. Information Sciences (2003) (in print)
Kulshreshtha, P., Shekar, B.: Interrelationships among fuzzy preference-based choice functions and significance of rationality conditions: A taxonomic and intuitive perspective. Fuzzy Sets and Systems 109, 429–4459 (2000)
Mirkin, B.G.: The Problem of Group Choice. Nauka Publ., Moscow (1974) (in Russian)
Orlovsky, S.A.: Decision-making with a fuzzy preference relation. Fuzzy Sets and Systems 1, 155–167 (1978)
Sheremetov, L., Romero-Cortés, J.: Fuzzy Coalition Formation Among Rational Cooperative Agents. In: Mařík, V., Müller, J.P., Pěchouček, M. (eds.) CEEMAS 2003. LNCS (LNAI), vol. 2691, p. 268. Springer, Heidelberg (2003)
Yager, R.: Fusion of multi-agent preference orderings. Fuzzy Sets and Systems 117, 1–12 (2001)
Zadeh, L.A.: Similarity relations and fuzzy orderings. Inform. Sciences 3, 177–200 (1971)
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Batyrshin, I., Shajdullina, N., Sheremetov, L. (2004). Strict Valued Preference Relations and Choice Functions in Decision-Making Procedures. In: Monroy, R., Arroyo-Figueroa, G., Sucar, L.E., Sossa, H. (eds) MICAI 2004: Advances in Artificial Intelligence. MICAI 2004. Lecture Notes in Computer Science(), vol 2972. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24694-7_34
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DOI: https://doi.org/10.1007/978-3-540-24694-7_34
Publisher Name: Springer, Berlin, Heidelberg
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