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Fuzzy Approach to Correlation Function

  • Bohdan S. Butkiewicz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4029)

Abstract

The paper presents second author’s step toward building quite new theory of fuzzy signals. Before, in the first step author defined fuzzy Fourier transform. Here, an approach to description of fuzzy correlation functions is proposed. New definitions, called later fuzzy correlation and defuzzified correlation are proposed for fuzzy signals. The definitions are based on new concepts of the class L \(_{f}^{\rm 2}\), L \(_{Tf}^{\rm 2}\), and class M f for fuzzy functions. Comparison with conventional approach and an example are shown.

Keywords

Correlation Function Membership Function Scalar Product Autocorrelation Function Signal Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Butkiewicz, B.S.: Fuzzy Approach to Fourier Transform. In: Signal Processing Symposium, Wilga, Poland, June 3-6, 1–6 (2005)Google Scholar
  2. 2.
    Butkiewicz, B.S.: An Approach to Theory of Fuzzy Signals, Basic Definitions. Paper sent to IEEE Transactions on Fuzzy SystemsGoogle Scholar
  3. 3.
    Butkiewicz, B.S.: Fuzzy Approach to Fourier Transform. Proceedings of SPIE 6159, 1045–1050 (2006)CrossRefGoogle Scholar
  4. 4.
    Dieudonné, J.: Foundations of Modern Analysis. Academic Press, London (1960)MATHGoogle Scholar
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    Zadeh, L.A.: The Concept of a Linguistic Variable and its Application to Approximate Reasoning. Part 1, Information Sciences 8, 199–249 (1975)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bohdan S. Butkiewicz
    • 1
  1. 1.Warsaw University of TechnologyWarsawPoland

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