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Soft Computing
Published in: Soft Computing 13/2017

01-06-2017 | Focus

Approximation by multivariate higher degree F-transform based on B-splines

Authors: Martins Kokainis, Svetlana Asmuss

Published in: Soft Computing | Issue 13/2017

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Abstract

The paper deals with the integral and discrete versions of the direct and inverse higher degree fuzzy transforms (F-transforms) of multivariate functions. The aim is to generalize to the multidimensional case the results known for the univariate F-transforms with respect to a generalized fuzzy partition given by B-splines. We prove that using multivariate B-splines as the generating functions of multidimensional fuzzy partition allows to improve the quality of approximation of multivariate functions and their derivatives.
previous article Weighted transform and approximation of some functions on unbounded sets
next article Continuous and discrete higher-degree F-transforms based on B-splines

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Footnotes
1
More precisely, of \( 2^d k_1 \ldots k_d \cdot \left( {\begin{array}{c}d+m\\ d\end{array}}\right) = O(1) \) such summands.
 
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Metadata
Title
Approximation by multivariate higher degree F-transform based on B-splines
Authors
Martins Kokainis
Svetlana Asmuss
Publication date
01-06-2017
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 13/2017
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2654-z

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