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 |
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| Deposited On: | 13 Nov 2012 11:25 |
| Last Modified: | 13 Nov 2012 11:25 |
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