Abstract
One of the main tasks in the theory of n-person transferable utility games is bound with looking for optimal solution concept. In general, a core is considered to be one of basic used solution concepts. The idea behind core derivation is straightforward; however, in reality uncertainty issues should be taken into consideration. Hence, the main aim of this article is to introduce formalization of the n-person transferable utility games in the case when expected utilities are intuitionistic fuzzy values. Moreover, this article discusses superadditivity issues of intuitionistic fuzzy extensions of cooperative games, and the construction of a core of such games. Calculations are demonstrated on numerical examples and compared with classical game theory results.
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References
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)
Anzilli, L.L., Facchinetti, G., Mastroleo, G.: Evaluation and ranking of intuitionistic fuzzy quantities. In: Masulli, F., Pasi, G., Yager R. (eds.) WILF 2013, LNAI, vol. 8256, pp. 139–149, Springer International Publishing Switzerland (2013)
Burillo, P., Bustince, H., Mohedano, V.: Some definitions of intuitionistic fuzzy number. First properties. In: Proceedings of the 1st Workshop on Fuzzy Based Expert Systems, pp. 53–55 (1994)
Coker, D.: An Introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst. 88(1), 81, 89 (1997)
Grzegorzewski, P.: Distances and orderings in a family of intuitionistic fuzzy numbers. In: Wagenknecht, M., Hampel R. (eds.): Proceedings of EUSFLAT Conference 2003, pp. 223–227 (2003)
Li, D.-F.: Decision and game theory in management with intuitionistic fuzzy sets. Studies in fuzziness and Soft computing, vol. 308, Springer, Heidelberg (2014)
Mahapatra, G.S., Roy, T.K.: Intuitionistic fuzzy number and its arithmetic operation with application on system failure. J. Uncertain. Syst. 7(2), 92–107 (2013)
Mareš, M.: Weak Arithmetics of fuzzy numbers. Fuzzy Sets Syst. 91, 143–153 (1997)
Mareš, M.: Additivities in fuzzy coalition games with side-payments. Kybernetika 35(2), 149–166 (1999)
Mareš, M.: Fuzzy Cooperative Games: Cooperation with Vague Expectations. Phisica-Verlag, Heilderberg (2001)
Parvathi, R., Malathi, C.: Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers. Int. J. Soft Comput. Eng. 2(2), 268–273 (2012)
Shoham, Y., Leyton-Brown, K.: Multiagent systems: algorithmic, game-theoretic, and logical foundations. Cambridge University Press, Cambridge (2009)
Wooldridge, M.J.: An introduction to multiagent systems. Wiley, New York (2002)
Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15, 1179–1187 (2007)
Xu, Z.S., Xia, M.: Induced generalized intuitionistic fuzzy operators. Knowl.-Based Syst. 24, 197–209 (2011)
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This paper was supported by the Ministry of Education, Youth and Sports within the Institutional Support for Long-term Development of a Research Organization in 2015.
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Mielcová, E. (2015). Core of n-Person Transferable Utility Games with Intuitionistic Fuzzy Expectations. In: Jezic, G., Howlett, R., Jain, L. (eds) Agent and Multi-Agent Systems: Technologies and Applications. Smart Innovation, Systems and Technologies, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-319-19728-9_14
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DOI: https://doi.org/10.1007/978-3-319-19728-9_14
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