%0 Book Section
%T On the k-additive Core of Capacities
publisher University of Ostrava
%D 2007
%U 978-80-7368-386-3
%@ https://hdl.handle.net/20.500.14352/53170
%X 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 thatassociated 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.
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