Previous |  Up |  Next


coalitional preferences; fuzzy game; optimization
The paper deals with the concept of coalitional preferences in the group decision-making situations in which the agents and coalitions have only vague idea about the comparative acceptability of particular outcomes. The coalitional games with vague utilities (see, e. g., [6]) can serve for a good example when some types of the game solutions (e. g., the von Neumann– Morgenstern one) are to be extended to the fuzzy game case. In this paper, we consider the fuzzy analogies of coalitional preferences and coalitional domination concepts known from the deterministic optimization models. These coalitional preferences are derived from the individual preferences of the coalition members. In the fuzzy extension of the model the input individual preferences are represented by fuzzy relations and, consequently, also the coalitional preferences have to be fuzzy. The general properties of these coalitional preferences are discussed in this contribution, and they are compared with the situation in the deterministic model. Finally, the case when the fuzziness of the individual preferences follows from fuzziness of the utility functions over the outcomes of the decision-making is mentioned and discussed.
[1] Dubois D., Kerre E. E., Mesiar, R., Prade H.: Fuzzy interval analysis. In: Fundamentals of Fuzzy Sets (D. Dubois and H. Prade, eds.), Kluwer, Dordrecht 2000, pp. 483–581 MR 1890240 | Zbl 0988.26020
[2] Kerre E. E., Wang X.: Reasonable properties for the ordering of fuzzy quantities. Part I. Fuzzy Sets and Systems 118 (2001), 375–383 MR 1809386 | Zbl 0971.03055
[3] Kerre E. E., Wang X.: Reasonable properties for the ordering of fuzzy quantities. Part II. Fuzzy Sets and Systems 118 (2001), 387–405 MR 1809387 | Zbl 0971.03055
[4] Luce J. R., Raiffa H.: Games and Decisions. Wiley, London 1957 Zbl 1233.91002
[5] Mareš M.: Computation Over Fuzzy Quantities. CRC–Press, Boca Raton 1994 MR 1327525 | Zbl 0859.94035
[6] Mareš M.: Weak arithmetics of fuzzy numbers. Fuzzy Sets and Systems 91 (1997), 143–154 DOI 10.1016/S0165-0114(97)00136-X | MR 1480041
[7] Mareš M.: Fuzzy Cooperative Games. Physica–Verlag, Heidelberg 2001 MR 1841340 | Zbl 1037.91007
[8] Neuman J. von, Morgenstern O.: Theory of Games and Economic Behaviour. Princeton Univ. Press, Princeton, N.J. 1953
[9] Rosenmüller J.: The Theory of Games and Markets. North Holland, Amsterdam 1982 MR 0632834 | Zbl 0464.90089
Partner of
EuDML logo