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

  • Linh NguyenEmail author
  • Michal Holčapek
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 643)


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.


Fuzzy transform Stationary process Noise reduction 



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.


  1. 1.
    Beran, J., Feng, Y., Ghosh, S., Kulik, R.: Long-Memory Processes: Probabilistic Properties and Statistical Methods, 1st edn. Springer, Heidelberg (2013)CrossRefzbMATHGoogle Scholar
  2. 2.
    Holčapek, M., Nguyen, L.: Trend-cycle estimation using fuzzy transform of higher degree. Iranian J. Fuzzy Syst. (2017)Google Scholar
  3. 3.
    Holčapek, M., Nguyen, L., Tichý, T.: Polynomial alias higher degree fuzzy transform of complex-valued functions. Fuzzy Sets Syst. (2016). doi: 10.1016/j.fss.2017.06.011, (submitted)
  4. 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)MathSciNetCrossRefGoogle Scholar
  5. 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)Google Scholar
  6. 6.
    Holčapek, M., Novák, V., Perfilieva, I.: Noise reduction in time series using F-transform. In: Proceedings of IEEE International Conference on Fuzzy Systems (2013). doi: 10.1109/FUZZ-IEEE.2013.6622492
  7. 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)CrossRefGoogle Scholar
  8. 8.
    Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157, 993–1023 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Perfilieva, I., Daňková, M., Bede, B.: Towards a higher degree F-transform. Fuzzy Sets Syst. 180, 3–19 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 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)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute for Research and Applications of Fuzzy Modelling, NSC IT4InnovationsUniversity of OstravaOstrava 1Czech Republic

Personalised recommendations