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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Official URL: http://www.eusflat.org/proceedings/EUSFLAT_2007/papers/Michel_Grabisch_(138).pdf

## 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 |
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Uncontrolled Keywords: | k-additive capacity, core, belief function |

Subjects: | Sciences > Mathematics > Topology |

ID Code: | 17056 |

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Deposited On: | 13 Nov 2012 10:25 |

Last Modified: | 07 Feb 2014 09:41 |

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