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On the k-additive Core of Capacities

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Grabisch, Michel and Miranda Menéndez, Pedro (2007) On the k-additive Core of Capacities. In New Dimensions in Fuzzy Logic and Related Technologies. Proceedings of the 5th EUSFLAT Conference, Ostrava, Czech Republic, September 11-14, 2007. University of Ostrava, Ostrava, pp. 257-263. ISBN 978-80-7368-386-3

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Abstract

We investigate in this paper the set of k-additive capacities dominating a given capacity,which we call the k-additive core. We study its structure through achievable families, which play the role of maximal chains in the classical case (k = 1), and show that
associated capacities are elements (possibly a vertex) of the k-additive core when the capacity is (k+1)-monotone. As a particular case, we study the set of k-additive belief functions dominating a belief function. The problem of finding all vertices of the k-additive core is still an open question.


Item Type:Book Section
Uncontrolled Keywords:k-additive capacity, core, belief function
Subjects:Sciences > Mathematics > Topology
ID Code:17056
Deposited On:13 Nov 2012 10:25
Last Modified:21 Jun 2018 10:57

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