title: |
On extension of fuzzy measures to aggregation functions |
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publication: |
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part of series: |
Advances in Intelligent Systems Research | |
| pages: | 28 - 32 | |
DOI: |
To be assigned soon (how to use a DOI) | |
author(s): |
Anna Koles¨¢rov¨¢, Andrea Stup¨¾anov¨¢, Juliana Beganov¨¢ |
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publication date: |
July 2011 |
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keywords: |
Aggregation function, Choquet integral, copula, fuzzy measure, n-monotone function,
quasi-copula, Archimedean quasi-copula |
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abstract: |
In the paper we study a method extending fuzzy
measures on the set N = {1, . . ., n} to n-ary aggregation functions on the interval [0, 1]. The method
is based on a fixed suitable n-ary aggregation function and the Möbius transform of the considered
fuzzy measure. This approach generalizes the wellknown Lovász and Owen extensions of fuzzy measures. We focus our attention on the special class
of n-dimensional Archimedean quasi-copulas and
prove characterization of all suitable n-dimensional
Archimedean quasi-copulas. We also present a special universal extension method based on a suitable
associative binary aggregation function. Several examples are included. |
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copyright: |
©
Atlantis Press. This article is distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |