Abstract
The paper presents an approach to description of fuzzy discrete functions and Fourier transform of such functions taking in consideration their uncertainty. Conventional approach to uncertainty employs probabilistic description. Here, fuzzy logic theory is applied to describe this uncertainty. A definition of transform, called later Discrete Fuzzy Fourier Transform and definition of Inverse Discrete Fuzzy Fourier Transform are proposed. Some properties of such transformations and examples of applications and comparison with conventional approach are shown.
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References
Bezdek, J.C., Pal, S.K.: Fuzzy Models for Pattern Recognition. IEEE Press, New York (1992)
Butkiewicz, B.S.: Fuzzy approach to Fourier transform. In: Proceedings of SPIE, vol. 6159, pp. 1045–1050 (2006)
Butkiewicz, B.S.: Fuzzy approach to correlation function. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 202–211. Springer, Heidelberg (2006)
Butkiewicz, B.S.: Fuzzy description of image processing. Proceedings of SPIE (to appear)
Butkiewicz, B.S.: Towards Fuzzy Fourier Transform. In: Eleventh Int. Conf. Information Processing and Management of Uncertainty in Knowledge-based Systems, Paris, pp. 2560–2565 (2006)
Butkiewicz, B.S.: Linguistic Fourier Transform and Fuzzy Image Description. In: Zittau Fuzzy Colloquium, Zittau, Germany, pp. 73–78 (2006)
Carleman, T.: L’Intégrale de Fourier et questions qui s’y rattachent. Almqvist and Wiksells, Uppsala (1944)
Dubois, D., Prade, H.: Fuzzy Sets and Systems. Academic Press, New York (1980)
Kosko, B.: Fuzzy engineering. Prentice Hall International, Englewood Cliffs (1997)
Nachtegael, M., Van der Weken, D., Van De Ville, D., Kerre, E.E. (eds.): Fuzzy Filters for Image Processing. Springer, Berlin (2003)
Haldeeva, E., Perfilieva, I.: Fuzzy Transformation. In: Joint 9th IFSA World Congress and 20th NAFIP Int. Conf., Vancouver, pp. 1946–1948 (2001)
Sugeno, M.: Fuzzy Systems with Undelying Deterministic Systems (Towards Fuzzy descriptions of Complex Systems). Res. Rep. L.A.A.S., Toulouse, France (1977)
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Butkiewicz, B.S. (2007). An Approach to Theory of Fuzzy Discrete Signals. In: Melin, P., Castillo, O., Aguilar, L.T., Kacprzyk, J., Pedrycz, W. (eds) Foundations of Fuzzy Logic and Soft Computing. IFSA 2007. Lecture Notes in Computer Science(), vol 4529. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72950-1_64
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DOI: https://doi.org/10.1007/978-3-540-72950-1_64
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72917-4
Online ISBN: 978-3-540-72950-1
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