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

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Advances in Fuzzy Logic and Technology 2017 (EUSFLAT 2017, IWIFSGN 2017)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 643))

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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Notes

  1. 1.

    These are more natural than which were considered in the early investigations.

  2. 2.

    This inequality is equivalent to the fact that .

  3. 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]).

References

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Acknowledgments

This work was supported by the project LQ1602 IT4Innovations excellence in science. The additional support was provided by the Czech Science Foundation through the project of No.16-09541S.

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Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modelling, NSC IT4Innovations, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Linh Nguyen & Michal Holčapek

Authors
  1. Linh Nguyen
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  2. Michal Holčapek
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Corresponding author

Correspondence to Linh Nguyen .

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Editors and Affiliations

  1. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

  2. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Eulalia Szmidt

  3. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Slawomir Zadrożny

  4. Institute of Biophysics and Biomedical Engineering, Department of Bioinformatics and Mathematical Modelling, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  5. WIT - Warsaw School of Information Technology, Warsaw, Poland

    Maciej Krawczak

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Nguyen, L., Holčapek, M. (2018). Higher Degree Fuzzy Transform: Application to Stationary Processes and Noise Reduction. In: Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K., Krawczak, M. (eds) Advances in Fuzzy Logic and Technology 2017. EUSFLAT IWIFSGN 2017 2017. Advances in Intelligent Systems and Computing, vol 643. Springer, Cham. https://doi.org/10.1007/978-3-319-66827-7_1

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

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-66826-0

  • Online ISBN: 978-3-319-66827-7

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