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Approximation Spaces in Rough Neurocomputing

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Rough Set Theory and Granular Computing

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 125))

Abstract

In the paper we discuss approximation spaces relevant for rough-neuro computing.

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References

  1. P. Doherty, W. Lukaszewicz, A. Skowron, and A. Szalas. Combining rough and crisp knowledge in deductive databases. 2001 (submitted to [4]).

    Google Scholar 

  2. T.M. Mitchell. Machine Learning. Mc Graw-Hill, Portland, 1997.

    MATH  Google Scholar 

  3. S.K. Pal, W. Pedrycz, A. Skowron, and R. Swiniarski, editors. Rough-Neuro Computing (special issue), volume 36. Elsevier, 2001.

    Google Scholar 

  4. S.K. Pal, L. Polkowski, and A. Skowron, editors. Rough-Neuro Computing: Techniques for Computing with Words. Springer-Verlag, Berlin, 2002. (in preparation).

    MATH  Google Scholar 

  5. Z. Pawlak. Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Dordrecht, 1991.

    MATH  Google Scholar 

  6. L. Polkowski and A. Skowron. Rough mereology: a new paradigm for approximate reasoning. International J. Approximate Reasoning, 15/4:333–365, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  7. L. Polkowski and A. Skowron, editors. Rough Sets in Knowledge Discovery Vol.1–2, Physica-Verlag, Heidelberg, 1998.

    Google Scholar 

  8. L. Polkowski and A. Skowron. Towards adaptive calculus of granules. In [17], pages 201–227, 1999.

    Google Scholar 

  9. L. Polkowski and A. Skowron. Rough-neuro computing. Lecture Notes in Artificial Intelligence, pages 25–32, 2001.

    Google Scholar 

  10. A. Skowron. Rough sets in KDD. In Z. Shi, B. Faltings, and M. Musem, editors, 16-th World Computer Congress (IFIP’2000):Proceedings of Conference on Intelligent Information Processing (IIP2000), pages 1–17, Beijing, 2000. Publishing House of Electronic Industry. (plenary talk).

    Google Scholar 

  11. A. Skowron. Toward intelligent systems: Calculi of information granules. Bulletin of the International Rough Set Society, 5/1–2:9–30, 2001.

    Google Scholar 

  12. A. Skowron and J. Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27:245–253, 1996.

    MathSciNet  MATH  Google Scholar 

  13. A. Skowron and J. Stepaniuk. Information granules: Towards foundations of granular computing. International Journal of Intelligent Systems, 16/1:57–86, 2001.

    Article  MATH  Google Scholar 

  14. L.A. Zadeh. Fuzzy logic = computing with words. IEEE Trans. on Fuzzy Systems, 4:103–111, 1996.

    Article  Google Scholar 

  15. L.A. Zadeh. Toward a theory of fuzzy information granulation and its certainty in human reasoning and fuzzy logic. Fuzzy Sets and Systems, 90:111–127, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  16. L.A. Zadeh. A new direction in ai: Toward a computational theory of perceptions. AI Magazine, 22/1:73–84, 2001.

    Google Scholar 

  17. L.A. Zadeh and J. Kacprzyk, editors. Computing with Words in Information/Intelligent Systems, volume 1–2. Physica-Verlag, Heidelberg, 1999.

    Google Scholar 

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Author information

Authors and Affiliations

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

    Andrzej Skowron

Authors
  1. Andrzej Skowron
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Editor information

Editors and Affiliations

  1. Graduate School of Engineering, Osaka University, Yamada-Oka, Suita 2-1, 565-0871, Osaka, Japan

    Masahiro Inuiguchi

  2. Shimane Medical University, Enya-Cho 89-1, 693-8501, Izumo, Shimane-ken, Japan

    Shoji Hirano  & Shusaku Tsumoto  & 

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© 2003 Springer-Verlag Berlin Heidelberg

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Skowron, A. (2003). Approximation Spaces in Rough Neurocomputing. In: Inuiguchi, M., Hirano, S., Tsumoto, S. (eds) Rough Set Theory and Granular Computing. Studies in Fuzziness and Soft Computing, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36473-3_2

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  • DOI: https://doi.org/10.1007/978-3-540-36473-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-05614-7

  • Online ISBN: 978-3-540-36473-3

  • eBook Packages: Springer Book Archive

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