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On the k-additive Core of Capacities


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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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

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