Miranda Menéndez, Pedro and Grabisch, Michel
*On vertices of the k-additive monotone core.*
In
IFSA-EUSFLAT 2009 Proceedings.
International Fuzzy Systems Association (IFSA); European Society for Fuzzy Logic and Technology (EUSFLAT), pp. 76-81.
ISBN 978-989-95079-6-8

PDF
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Official URL: http://www.eusflat.org/proceedings/IFSA-EUSFLAT_2009/pdf/tema_0076.pdf

## Abstract

Given a capacity, the set of dominating k-additive capacities is a convex polytope; 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 k-additive monotone core. Then, we characterize the vertices of the n-additive core and finally, we explore the possible translations for the k-additive case

Item Type: | Book Section |
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Additional Information: | Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009. |

Uncontrolled Keywords: | Keywords—Capacities, k-additivity, dominance, core |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 16957 |

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Deposited On: | 31 Oct 2012 09:42 |

Last Modified: | 31 Oct 2012 09:42 |

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