Higher Degree Fuzzy Transform: Application to Stationary Processes and Noise Reduction
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.
KeywordsFuzzy 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.
- 2.Holčapek, M., Nguyen, L.: Trend-cycle estimation using fuzzy transform of higher degree. Iranian J. Fuzzy Syst. (2017)Google Scholar
- 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)
- 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.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
- 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