A study of the k-additive core of capacities through achievable
families
Résumé
We investigate in this paper about 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 element
(possibly a vertex) of the $k$-additive core when the capacity is
$(k+1)$-monotone. The problem of finding all vertices of the $k$-additive core
is still an open question.
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 element
(possibly a vertex) of the $k$-additive core when the capacity is
$(k+1)$-monotone. The problem of finding all vertices of the $k$-additive core
is still an open question.