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Transactions on Rough Sets II pp 63–81Cite as

Fuzzy Transforms

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Part of the book series: Lecture Notes in Computer Science ((TRS,volume 3135))

Abstract

The technique of direct and inverse F–transforms is introduced and approximating properties of the inverse F–transform are described. Numerical methods based on fuzzy approximation models are developed. Among them are numeric integration and approximate solution of ordinary differential equations (the Cauchy problem). Advantages of the new technique based on F–transforms over some classical numeric methods are demonstrated on examples.

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References

  1. Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer, Dordrecht (1999)

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  2. Perfilieva, I.: Logical approximation: General approach to the construction of approximating formulas. In: Proceedings EUSFLAT 2001, Leicester, Great Britain, pp. 9–11 (2001)

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  5. Perfilieva, I.: Logical approximation. Soft Computing 7 (2003) (to appear)

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  6. Perfilieva, I., Chaldeeva, E.: Fuzzy transformation. In: Proceedings IFSA 2001 World Congress, Vancouver, Canada (2001)

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Author information

Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1, Czech Republic

    Irina Perfilieva

Authors
  1. Irina Perfilieva
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Manitoba, R3T 5V6, Winnipeg, Manitoba, Canada

    James F. Peters

  2. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  3. Institut de Recherche en Informatique de Toulouse, France

    Didier Dubois

  4. Institute of Computer Science, Polish Academy of Sciences, 01–237, Warsaw, Poland

    Jerzy W. Grzymała-Busse

  5. Department of Systems Innovation, Graduate School of Engineering Science, Osaka University, 1-3, Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

  6. Polish-Japanese Institute of Information Technology Warsaw, Poland Department of Mathematics and Computer Science, University of Warmia and Mazury, Olsztyn, Poland

    Lech Polkowski

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© 2004 Springer-Verlag Berlin Heidelberg

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Perfilieva, I. (2004). Fuzzy Transforms. In: Peters, J.F., Skowron, A., Dubois, D., Grzymała-Busse, J.W., Inuiguchi, M., Polkowski, L. (eds) Transactions on Rough Sets II. Lecture Notes in Computer Science, vol 3135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27778-1_5

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  • DOI: https://doi.org/10.1007/978-3-540-27778-1_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23990-1

  • Online ISBN: 978-3-540-27778-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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