Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32127
The Banzhaf-Owen Value for Fuzzy Games with a Coalition Structure

Authors: Fan-Yong Meng


In this paper, a generalized form of the Banzhaf-Owen value for cooperative fuzzy games with a coalition structure is proposed. Its axiomatic system is given by extending crisp case. In order to better understand the Banzhaf-Owen value for fuzzy games with a coalition structure, we briefly introduce the Banzhaf-Owen values for two special kinds of fuzzy games with a coalition structure, and give their explicit forms.

Keywords: Cooperative fuzzy game, Banzhaf-Owen value, multi linear extension, Choquet integral.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1382


[1] G. Owen, Values of games with a priori unions, Springer-Verlag, Nueva York, 1977.
[2] G. Owen, Characterization of the Banzhaf-Coleman index, SIAM Journal on Applied Mathematics 35 (1978) 315-327.
[3] J. M. Alonso-Meijde and M. G. Fiestras-Janeiro, Modification of the Banzhaf value for games with a coalition structure, Annals of Operations Research 109 (2002) 213-227.
[4] M. J. Albizuri, Axiomatizations of the Owen value without efficiency, Mathematical Social Sciences 55 (2008) 78-89.
[5] J. M. Alonso-Meijide, F. Carreras, M. G. Fiestras-Janeiro and G. Owen, A comparative axiomatic characterization of the Banzhaf-Owen coalitional value, Decision Support Systems 43 (2007) 701-712.
[6] R. Amer, F. Carreras and J. M. Gimenez, The modified Banzhaf value for games with coalition structure: an axiomatic characterization, Mathematical Social Sciences 43 (2002) 45-54.
[7] G. Hamiache, A new axiomatization of the Owen value for games with coalition structures, Mathematical Social Sciences 37 (1999) 281-305.
[8] A. B. Khmelnitskaya and E. B. Yanovskaya, Owen coalitional value without additivity axiom, Mathematical Methods of Operations Research 66 (2007) 255-261.
[9] J. P. Aubin, Mathematical methods of game and economic theory, Rev. ed., North-Holland, Amsterdam, 1982.
[10] G. Owen, Multilinear extensions of games", Management Sciences 18 (1971) 64-79.
[11] M. Tsurumi, T. Tanino and M. Inuiguchi, A Shapley function on a class of cooperative fuzzy games, European Journal of Operational Research 129 (2001) 596-618.
[12] D. Butnariu, Stability and Shapley value for an n-persons fuzzy game, Fuzzy Sets and Systems 4 (1980) 63-72.
[13] D. Butnariu and T. Kroupa, Shapley mappings and the cumulative value for n-person games with fuzzy Coalitions, European Journal of Operational Research.186 (2008) 288-299.
[14] F. Y. Meng and Q. Zhang, The Shapley value on a kind of cooperative fuzzy games, Journal of Computational Information Systems 7 (2011)1846-1854.
[15] Y. A. Hwang, Fuzzy games: A characterization of the core, Fuzzy Sets and Systems 158 (2007) 2480-2493.
[16] Y. A. Hwang and Y. H. Liao, Max-consistency, complement- consistency and the core of fuzzy games, Fuzzy Sets and Systems159 (2008) 152- 163.
[17] S. Tijs, R. Branzei, S. Ishihara and S. Muto, On cores and stable sets for fuzzy games, Fuzzy Sets and Systems 146 (2004) 285-296.
[18] M. Sakawa and I. Nishizalzi, A lexicographical solution concept in an n-person cooperative fuzzy game, Fuzzy Sets and Systems 61 (1994) 265-275.
[19] X. H. Yu and Q. Zhang, The fuzzy core in games with fuzzy coalitions, Journal of Computational and Applied Mathematics 230 (2009)173-186.
[20] F. Y. Meng, Q. Zhang and J. Tang, The measure of interaction among T-fuzzy coalitions, Systems Engineering-Theory Practice 30 (2010) 73- 83. (in Chinese)
[21] F. Y. Meng and Q. Zhang, Fuzzy cooperative games with Choquet integral form, Systems Engineering and Electronics 32 (2010) 1430- 1436. (in Chinese)
[22] F. Y. Meng and Q. Zhang, The Shapley function for fuzzy cooperative games with multilinear extension form, Applied Mathematics Letters 23 (2010) 644-650.
[23] E. Lehrer, An axiomatization of the Banzhaf value, International Journal of Game Theory 17 (1988) 89-99.