On extension of fuzzy measures to aggregation functions

DOI

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.

Copyright

© 2011, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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 (EUSFLAT-11)
PB  - Atlantis Press
SP  - 28
EP  - 32
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.11
DO  - 10.2991/eusflat.2011.11
ID  - Kolesárová2011/08
ER  -