Miranda Menéndez, Pedro and Grabisch, Michel
*An algorithm for finding the vertices of the k-additive monotone core.*
Discrete Applied Mathematics, 160
.
pp. 628-639.
ISSN 0166-218X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0166218X1100463X

## Abstract

Given a capacity, the set of dominating k-additive capacities is a convex polytope called the k-additive monotone core; thus, it is defined by its vertices. In this paper, we deal with the problem of deriving a procedure to obtain such vertices in the line of the results of Shapley and Ichiishi for the additive case. We propose an algorithm to determine the vertices of the n-additive monotone core and we explore the possible translations for the k-additive case.

Item Type: | Article |
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Uncontrolled Keywords: | Polyhedra; Capacities; k-additivity; Dominance; Core |

Subjects: | Sciences > Statistics > Game theory |

ID Code: | 16860 |

References: | O. Bondareva, Some applications of linear programming to the theory of cooperative games, Problemy Kibernet 10 (1963) 119–139. A. Chateauneuf, J.-Y. Jaffray, Some characterizations of lower probabilities and other monotone capacities through the use of Möbius inversion, Math. Social Sci. 17 (1989) 263–283. G. Choquet, Theory of capacities, Annales de l’Institut Fourier 5 (1953) 131–295. E.F. Combarro, P. Miranda, Adjacency on the order polytope with applications to the theory of fuzzy measures, Fuzzy Sets and Systems 180 (2010) 384–398. E.F. Combarro, P. Miranda, On the structure of the k-additive fuzzy measures, Fuzzy Sets and Systems 161 (2010) 2314–2327. A.P. Dempster, Upper and lower probabilities induced by a multivalued mapping, The Annals of Mathematical Statististics 38 (1967) 325–339. D. Denneberg, Non-additive Measures and Integral, Kluwer Academic, Dordrecht, The Netherlands, 1994. T. Driessen, Cooperative Games, Kluwer Academic, 1988. D. Dubois, H. Prade, A class of fuzzy measures based on triangular norms, Internal Journal of General Systems 8 (1982) 43–61. M. Grabisch, Alternative representations of discrete fuzzy measures for decision making, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5 (1997) 587–607. M. Grabisch, k-order additive discrete fuzzy measures, in: Proceedings of 6th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, IPMU, Granada, Spain, 1996, pp. 1345–1350. M. Grabisch, k-order additive discrete fuzzy measures and their representation, Fuzzy Sets and Systems 92 (1997) 167–189. M. Grabisch, P. Miranda, On the vertices of the k-additive core, Discrete Math. 308 (2008) 5204–5217. J.C. Harsanyi, A simplified bargaining model for the n-person cooperative game, International Economic Review 4 (1963) 194–220. T. Ichiishi, Super-modularity: applications to convex games and to the Greedy algorithm for LP, Journal of Economic Theory 25 (1981) 283–286. J.-L. Marichal, Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral, European J. Oper. Res. 155 (3) (2004)771–791. P. Miranda, E.F. Combarro, On the structure of some families of fuzzy measures, IEEE Transactions on Fuzzy Systems 15 (6) (2007) 1068–1081. P. Miranda, E.F. Combarro, P. Gil, Extreme points of some families of non-additive measures, European J. Oper. Res. 33 (10) (2006) 3046–3066. P. Miranda, M. Grabisch, k-balanced games and capacities, European J. Oper. Res. 200 (2010) 465–472. P. Miranda, M. Grabisch, P. Gil, p-symmetric fuzzy measures, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 10 (Suppl.) (2002) 105–123. G. Owen, Game Theory, Academic Press, 1995. |

Deposited On: | 25 Oct 2012 08:41 |

Last Modified: | 25 Oct 2012 08:41 |

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