Molina Ferragut, Elisenda and Tejada Cazorla, Juan Antonio
(2002)
*The equalizer and the lexicographical solutions for cooperative fuzzy games: characterization and properties.*
Fuzzy Sets and Systems, 125
(3).
pp. 369-387.
ISSN 0165-0114

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Official URL: http://www.sciencedirect.com/science/article/pii/S0165011401000239

## Abstract

In this paper we analyze the lexicographical solution for fuzzy TU games, we study its properties and obtain a characterization. The lexicographical solution was introduced by Sakawa and Nishizaki (Fuzzy Sets and Systems 61 (1994) 265-275) as a solution for crisp TU games, and then extended as a value for fuzzy TU games. We approach the problem by means of the close relationship that exists between the lexicographical solution for crisp TU games and the least square nucleolus, a crisp value defined by Ruiz et al. (Internat. J. Game Theory 25 (1996) 113-134). Previously, and also based on this relationship, we axiomatically characterize the equalizer solution for fuzzy TU games. Both values, the equalizer and the lexicographical solutions, are based on the consideration of a measure of dissatisfaction of players rather than coalitions.

Item Type: | Article |
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Uncontrolled Keywords: | Decision making; Fuzzy TU games; Fuzzy coalitions; Coalition excess; Player excess; Lexicographical solution; Least square nucleolus and prenucleolus |

Subjects: | Sciences > Mathematics > Operations research |

ID Code: | 15939 |

References: | J.P. Aubin, Coeur et valeur des jeux Tous Ua paiements latVeraux, C.R. Acad. Sci. Paris 279 A (1974) 891–894. J.P. Aubin, Mathematical Methods of Game and Economic Theory, North-Holland, Amsterdam, 1980. J.P. Aubin, Cooperative fuzzy games, Math. Oper. Res. 6 (1981) 1–13. J.F. Banzhaf, Weighted voting doesn’t work: a mathematical analysis, Rutgers Law Rev. 19 (1965) 317–343. A. Billot, Fuzzy convexity and peripheral core of an exchange economy represented as a fuzzy game, in: J. Kacprzyk, M. Fedrizzi (Eds.), Multipersons Decision Making Models using Fuzzy Sets and Possibility Theory, Kluwer, Dordrecht, 1990. D. Butnariu, Fuzzy games: a description of the concept, Fuzzy Sets and Systems 1 (1978) 181–192. J.S. Coleman, Control of collectivities and the power of a collectivity to act, in: B. Lieberman (Ed.), Social Choice, Gordon and Breach, London, 1971. S. Hart, A. Mas-Colell, Potential, value and consistency, Econometrica 57 (1989) 589–614. G. Owen, Multilinear extensions of games, Manag. Sci. 18 (1972) 64–79. L.M. Ruiz, F. Valenciano, J.M. Zarzuelo, The least square prenucleolus and the least square nucleolus. Two values for TU games based on the excess vector, Internat. J. Game Theory 25 (1996) 113–134. M. Sakawa, I. Nishizaki, A lexicographical concept in an n-person cooperative fuzzy game, Fuzzy Sets and Systems 61 (1994)265–275. D. Schmeidler, The nucleolus of a characteristic function game, SIAM J. Appl. Math. 17 (1969) 1163–1170. L.S. Shapley, A value for n-person games, in: H.W. Kuhn, A.W. Tucker (Eds.), Annals of Mathematical Studies, Vol. 28, Academic Press, Princeton, 1953, pp. 307–317. L.S. Shapley, M. Shubik, On market games, J. Econom. Theory 1 (1969) 9–25. A.I. Sobolev, The functional equations that give the payoIs of the players in an n-person game, Math. Methods Social Sci. 6 (1975) 94–151. J. Tejada, Juegos Difusos, Tesis Doctorales 171=92, Universidad Complutense, Madrid, 1986. H.P. Young, Monotonic solutions of cooperative games, Internat. J. Game Theory 14 (1985) 65–72. |

Deposited On: | 13 Jul 2012 07:38 |

Last Modified: | 06 Feb 2014 10:34 |

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