Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)

On extension of fuzzy measures to aggregation functions

Authors
Anna Kolesárová, Andrea Stupnanová, Juliana Beganová
Corresponding Author
Anna Kolesárová
Available Online August 2011.
DOI
https://doi.org/10.2991/eusflat.2011.11How to use a DOI?
Keywords
Aggregation function, Choquet integral, copula, fuzzy measure, n-monotone function, quasi-copula, Archimedean quasi-copula
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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Proceedings
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
Part of series
Advances in Intelligent Systems Research
Publication Date
August 2011
ISBN
978-90-78677-00-0
DOI
https://doi.org/10.2991/eusflat.2011.11How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Anna Kolesárová
AU  - Andrea Stupnanová
AU  - Juliana Beganová
PY  - 2011/08
DA  - 2011/08
TI  - On extension of fuzzy measures to aggregation functions
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 28
EP  - 32
UR  - https://doi.org/10.2991/eusflat.2011.11
DO  - https://doi.org/10.2991/eusflat.2011.11
ID  - Kolesárová2011/08
ER  -