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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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.
|Uncontrolled Keywords:||Fuzzy measures; k-Additive measures; Vertices|
|Subjects:||Sciences > Mathematics > Topology|
|Deposited On:||29 Oct 2012 11:08|
|Last Modified:||29 Oct 2012 11:08|
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