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Soft Computing
Erschienen in: Soft Computing 13/2017

03.06.2017 | Focus

Multivariate fuzzy transform of complex-valued functions determined by monomial basis

verfasst von: Linh Nguyen, Michal Holčapek, Vilém Novák

Erschienen in: Soft Computing | Ausgabe 13/2017

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Abstract

In this paper, we introduce the multivariate fuzzy transform of higher degree of complex-valued functions. Apart from the orthogonal bases of multivariate complex polynomials of weighted Hilbert spaces that are derived by the Gram–Schmidt orthogonalization process, which can be problematic and imprecise in certain cases, we propose to compute the multivariate fuzzy transform components using a simple matrix calculus with the help of the monomial bases. By this novel approach, we derive two types of upper bound of the approximation error both of multivariate complex-valued functions and of their partial derivatives (the latter by the multivariate higher degree fuzzy transform). The results are demonstrated on examples.
Vorheriger Artikel Continuous and discrete higher-degree F-transforms based on B-splines
Nächster Artikel An adaptive image filter based on the fuzzy transform for impulse noise reduction

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Fußnoten
1
It means that the real part as well as the imaginary part is bounded piecewise continuous real-valued n-variate functions.
 
2
Note that a fair comparison of methods is beyond of the scope of this paper, because a suitable choice of the parameters of the respective method can significantly influence the quality of particular approximation. A preliminary comparison of methods with the univariate higher degree F-transform can be found in Holčapek et al. (2016).
 
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Metadaten
Titel
Multivariate fuzzy transform of complex-valued functions determined by monomial basis
verfasst von
Linh Nguyen
Michal Holčapek
Vilém Novák
Publikationsdatum
03.06.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Soft Computing / Ausgabe 13/2017
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2658-8

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