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2018 | OriginalPaper | Chapter

Higher Degree Fuzzy Transform: Application to Stationary Processes and Noise Reduction

Authors : Linh Nguyen, Michal Holčapek

Published in: Advances in Fuzzy Logic and Technology 2017

Publisher: Springer International Publishing

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Abstract

In this contribution, we first elaborate the theory of the fuzzy transform of higher degree (F\(^m\)-transform, \(m\ge 0\)) applied to stationary processes that was initiated by Holčapek et al. in [5, 6]. Then, we provide mathematical justification for its application to reduction of irregular fluctuations (noise) generated by specific stationary processes.

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next chapter Sheffer Stroke Fuzzy Implications
Footnotes
1
These are more natural than which were considered in the early investigations.
 
2
This inequality is equivalent to the fact that https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-66827-7_1/455375_1_En_1_IEq118_HTML.gif .
 
3
We use the name “short-memory” and “long-memory” stationary process only to distinguish two considered assumptions. And these names, somehow, characterize the behavior of the correlation function. By the aim of this paper, we do not further investigate the same concepts used in probability and statistic (see [1]).
 
Literature
1.
Beran, J., Feng, Y., Ghosh, S., Kulik, R.: Long-Memory Processes: Probabilistic Properties and Statistical Methods, 1st edn. Springer, Heidelberg (2013)CrossRefMATH
2.
Holčapek, M., Nguyen, L.: Trend-cycle estimation using fuzzy transform of higher degree. Iranian J. Fuzzy Syst. (2017)
3.
4.
Holčapek, M., Perfilieva, I., Novák, V., Kreinovich, V.: Necessary and sufficient conditions for generalized uniform fuzzy partition. Fuzzy Sets Syst. 277, 97–121 (2015)MathSciNetCrossRef
5.
Holčapek, M., Novák, V., Perfilieva, I.: Analysis of stationary processes using fuzzy transform. In: Proceedings of European Society for Fuzzy Logic and Technology, pp. 714–721 (2013)
6.
7.
Nguyen, L., Holčapek, M., Novák, V.: Multivariate fuzzy transform of complex-valued functions determined by monomial basis. Soft Computing 21(13), 3641–3658 (2017)CrossRef
8.
9.
10.
Yaglom, A. M.: An introduction to the theory of stationary random functions. Revised English ed. Translated and edited by R.A. Silverman. Prentice-Hall, Inc. XIII, Englewood Cliffs, NJ (1962)
Metadata
Title
Higher Degree Fuzzy Transform: Application to Stationary Processes and Noise Reduction
Authors
Linh Nguyen
Michal Holčapek
Copyright Year
2018
Book
Advances in Fuzzy Logic and Technology 2017

Print ISBN: 978-3-319-66826-0

Electronic ISBN: 978-3-319-66827-7

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-66827-7_1

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