Disjointness of fuzzy coalitions
Kybernetika (2008)
- Volume: 44, Issue: 3, page 416-429
- ISSN: 0023-5954
Access Full Article
top
Abstract
topHow to cite
topMareš, Milan, and Vlach, Milan. "Disjointness of fuzzy coalitions." Kybernetika 44.3 (2008): 416-429. <http://eudml.org/doc/33937>.
@article{Mareš2008,
abstract = {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.},
author = {Mareš, Milan, Vlach, Milan},
journal = {Kybernetika},
keywords = {fuzzy cooperative game; fuzzy coalition; vague cooperation; block of players; fuzzy cooperative game; fuzzy coalition; vague cooperation; block of players},
language = {eng},
number = {3},
pages = {416-429},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Disjointness of fuzzy coalitions},
url = {http://eudml.org/doc/33937},
volume = {44},
year = {2008},
}
TY - JOUR
AU - Mareš, Milan
AU - Vlach, Milan
TI - Disjointness of fuzzy coalitions
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 3
SP - 416
EP - 429
AB - 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.
LA - eng
KW - fuzzy cooperative game; fuzzy coalition; vague cooperation; block of players; fuzzy cooperative game; fuzzy coalition; vague cooperation; block of players
UR - http://eudml.org/doc/33937
ER -
References
top- Aubin J. P., Cooperative fuzzy games, Math. Oper. Res. 6 (1981), 1–13 (1981) Zbl0496.90092MR0618959
- Butnariu D., Fuzzy games: a description of the concept, Fuzzy Sets and Systems 1 (1978), 181–192 (1978) Zbl0389.90100MR0503928
- Butnariu D., Klement E. P., Triangular Norm–Based Measures and Games With Fuzzy Coalitions, Kluwer, Dordrecht 1993 Zbl0804.90145MR2867321
- Grabish M., The Shapley value for games on lattices (-fuzzy games), In: Proc. FSSCEF 2004, Sankt Petersburg, Russian Fuzzy Systems Association, St. Petersburg 2004, Vol. I, pp. 257–264
- Luce R. D., Raiffa H., Games and Decisions, Wiley, London 1957 Zbl1233.91002MR0087572
- Mareš M., Combinations and transformations of the general coalition games, Kybernetika 17 (1981), 1, 45–61 (1981) MR0629348
- Mareš M., Fuzzy Cooperative Games, Cooperation With Vague Expectations. Physica–Verlag, Heidelberg 2001 Zbl1037.91007MR1841340
- Mareš M., Computation Over Fuzzy Quantities, CRC–Press, Boca Raton 1994 Zbl0859.94035MR1327525
- 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 Zbl1153.91325
- Mareš M., Vlach M., Fuzzy coalitional structures, Mathware and Soft Computing, submitted Zbl1153.91325
- 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
- Mareš M., Vlach M., Alternative representation of fuzzy coalitions, Internat. J. Uncertainty, Fuzziness and Knowledge–Based Systems, submitted
- Rosenmüller J., The Theory of Games and Markets, North Holland, Amsterdam 1982 Zbl0464.90089MR0632834
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.