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

## 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 |
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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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