On the k-additive Core of Capacities

We investigate in this paper the set of kadditive 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.

• Type: Conference
• Year: 2007
• Where: EUSFLAT
• Authors: Michel Grabisch, Pedro Miranda
• Keywords: Belief Function, EUSFLAT 2007, K-additive Core, Kadditive Capacities