Article
Full entry |
PDF
(0.7 MB)
Feedback
PDF
(0.7 MB)
Feedback
Keywords:
fuzzy cooperative game; fuzzy coalition; vague cooperation; block of players
fuzzy cooperative game; fuzzy coalition; vague cooperation; block of players
Summary:
The cooperative games with fuzzy coalitions in which some players act in a coalition only with a fraction of their total “power” (endeavor, investments, material, etc.) or in which they can distribute their “power” in more coalitions, are connected with some formal or interpretational problems. Some of these problems can be avoided if we interpret each fuzzy coalition as a fuzzy class of crisp coalitions, as shown by Mareš and Vlach in [9,10,11]. The relation between this model of fuzziness and the original one, where fuzzy coalition is a fuzzy set of players, is shown and the properties of the model are analyzed and briefly interpreted in this paper. The analysis is focused on very elementary properties of fuzzy coalitions and their payments like disjointness, superadditivity and also convexity. Three variants of their modelling are shown and their consistency is investigated. The derived results may be used for further development of the theory of fuzzy coalitions characterized by fuzzy sets of crisp coalitions. They show that the procedure developed in [11] appears to be the most adequate.
References:
[1] Aubin J. P.: Cooperative fuzzy games. Math. Oper. Res. 6 (1981), 1–13 MR 0618959 | Zbl 0496.90092
[2] Butnariu D.: Fuzzy games: a description of the concept. Fuzzy Sets and Systems 1 (1978), 181–192 MR 0503928 | Zbl 0389.90100
[3] Butnariu D., Klement E. P.: Triangular Norm–Based Measures and Games With Fuzzy Coalitions. Kluwer, Dordrecht 1993 MR 2867321 | Zbl 0804.90145
[4] Grabish M.: The Shapley value for games on lattices ($L$-fuzzy games). In: Proc. FSSCEF 2004, Sankt Petersburg, Russian Fuzzy Systems Association, St. Petersburg 2004, Vol. I, pp. 257–264
[5] Luce R. D., Raiffa H.: Games and Decisions. Wiley, London 1957 MR 0087572 | Zbl 1233.91002
[6] Mareš M.: Combinations and transformations of the general coalition games. Kybernetika 17 (1981), 1, 45–61 MR 0629348
[7] Mareš M.: Fuzzy Cooperative Games. Cooperation With Vague Expectations. Physica–Verlag, Heidelberg 2001 MR 1841340 | Zbl 1037.91007
[8] Mareš M.: Computation Over Fuzzy Quantities. CRC–Press, Boca Raton 1994 MR 1327525 | Zbl 0859.94035
[9] Mareš M., Vlach M.: Fuzzy coalitional structures. In: Proc. 6th Czech–Japan Seminar on Methods for Decision Support in Environment with Uncertainty, Valtice 2003 (J. Ramík and V. Novák, eds.), University of Ostrava, Ostrava 2003 Zbl 1153.91325
[10] Mareš M., Vlach M.: Fuzzy coalitional structures. Mathware and Soft Computing, submitted Zbl 1153.91325
[11] Mareš M., Vlach M.: Fuzzy coalitions as fuzzy classes of crisp coalitions. In: Proc. 7th Japan–Czech Seminar on Decision–Making in Environment With Uncertainty, Awaji 2004, Osaka University, pp. 34–43
[12] Mareš M., Vlach M.: Alternative representation of fuzzy coalitions. Internat. J. Uncertainty, Fuzziness and Knowledge–Based Systems, submitted
[13] Rosenmüller J.: The Theory of Games and Markets. North Holland, Amsterdam 1982 MR 0632834 | Zbl 0464.90089
Search
Partner of
