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A New Insight into Entropy Based on the Fuzzy Operators, Applied to Useful Information Extraction from Noisy Time-Frequency Distributions

Author

Listed:
  • József Dombi

    (Department of Computer Algorithms and Artificial Intelligence, University of Szeged, 6720 Szeged, Hungary)

  • Ana Vranković Lacković

    (Faculty of Engineering, University of Rijeka, 51000 Rijeka, Croatia)

  • Jonatan Lerga

    (Faculty of Engineering, University of Rijeka, 51000 Rijeka, Croatia
    Center for Artificial Intelligence and Cybersecurity, University of Rijeka, 51000 Rijeka, Croatia)

Abstract

In this paper, we study the connections between generalized mean operators and entropies, where the mean value operators are related to the strictly monotone logical operators of fuzzy theory. Here, we propose a new entropy measure based on the family of generalized Dombi operators. Namely, this measure is obtained by using the Dombi operator as a generator function in the general solution of the bisymmetric functional equation. We show how the proposed entropy can be used in a fuzzy system where the performance is consistent in choosing the best alternative in the Multiple Attribute Decision-Making Problem. This newly defined entropy was also applied to the problem of extracting useful information from time-frequency representations of noisy, nonstationary, and multicomponent signals. The denoising results were compared to Shannon and Rényi entropies. The proposed entropy measure is shown to significantly outperform the competing ones in terms of denoising classification accuracy and the F1-score due to its sensitivity to small changes in the probability distribution.

Suggested Citation

  • József Dombi & Ana Vranković Lacković & Jonatan Lerga, 2023. "A New Insight into Entropy Based on the Fuzzy Operators, Applied to Useful Information Extraction from Noisy Time-Frequency Distributions," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:505-:d:1038992
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    References listed on IDEAS

    as
    1. Lamarche, Pierre, 2017. "Estimating consumption in the HFCS: Experimental results on the first wave of the HFCS," Statistics Paper Series 22, European Central Bank.
    2. B. Sharma & I. Taneja, 1975. "Entropy of type (α, β) and other generalized measures in information theory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 22(1), pages 205-215, December.
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