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On the structure of the k-additive fuzzy measures

Miranda Menéndez, Pedro and Combarro, Elías F. (2010) On the structure of the k-additive fuzzy measures. Fuzzy Sets and Systems, 161 (17). pp. 2314-2327. ISSN 0165-0114

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Official URL: http://www.sciencedirect.com/science/article/pii/S0165011410001351

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Abstract

In this paper we present some results concerning the vertices of the set of fuzzy measures being at most k-additive. We provide an algorithm to compute them. We give some examples of the results obtained with this algorithm and give lower bounds on the number of vertices for the (n - 1)-additive case, proving that it grows much faster than the number of vertices of the general fuzzy measures. The results in the paper suggest that the structure of k-additive measures might be more complex than expected from their definition and, in particular, that they are more complex than general fuzzy measures.

Item Type:Article
Uncontrolled Keywords:Fuzzy measures; k-Additive measures; Vertices
Subjects:Sciences > Mathematics > Topology
ID Code:16907
Deposited On:29 Oct 2012 10:08
Last Modified:07 Feb 2014 09:38

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