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On vertices of the k-additive monotone core

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

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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
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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Last Modified:31 Oct 2012 09:42

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