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Approximation Spaces and Information Granulation

  • Andrzej Skowron
  • Roman Swiniarski
  • Piotr Synak
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3066)

Abstract

We discuss approximation spaces in the granular computing framework. Such approximation spaces generalise the approaches to concept approximation existing in rough set theory. Approximation spaces are constructed as higher level information granules and are obtained as the result of complex modelling. We present illustrative examples of modelling approximation spaces including approximation spaces for function approximation, inducing concept approximation, and some other information granule approximations. In modelling of such approximation spaces we use an important assumption that not only objects but also more complex information granules involved in approximations are perceived using only partial information about them.

Keywords

Inclusion Function Approximation Space Concept Approximation Information Granule Granular Computing 
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.
    Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)zbMATHGoogle Scholar
  2. 2.
    Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27, 245–253 (1996)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Polkowski, L., Skowron, A.: Rough mereology:A new paradigm for approximate reasoning. International Journal of Approximate Reasoning 15, 333–365 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Polkowski, L., Skowron, A.: Towards adaptive calculus of granules. In: Zadeh, L.A., Kacprzyk, J. (eds.) Computing with Words in Information/Intelligent Systems, Heidelberg, Germany, pp. 201–227. Physica-Verlag (1999)Google Scholar
  5. 5.
    Skowron, A., Stepaniuk, J.: Information granules and rough-neural computing. In: [10], pp. 43–84 Google Scholar
  6. 6.
    Lin, T.Y.: The discovery, analysis and representation of data dependencies in databases. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 1: Methodology and Applications. Studies in Fuzziness and Soft Computing, vol. 18, pp. 107–121. Physica-Verlag, Heidelberg (1998)Google Scholar
  7. 7.
    Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46, 39–59 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Peters, J.F., Skowron, A., Synak, P., Ramanna, S.: Rough sets and information granulation. In: De Baets, B., Kaynak, O., Bilgiç, T. (eds.) IFSA 2003. LNCS, vol. 2715, pp. 370–377. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Skowron, A.: Toward intelligent systems: Calculi of information granules. Bulletin of the International Rough Set Society 5, 9–30 (2001)Google Scholar
  10. 10.
    Pal, S.K., Polkowski, L., Skowron, A. (eds.): Rough-Neural Computing: Techniques for Computing with Words. Cognitive Technologies. Springer, Heidelberg (2003)Google Scholar
  11. 11.
    Zadeh, L.A.: A new direction in AI: Toward a computational theory of perceptions. AI Magazine 22, 73–84 (2001)Google Scholar
  12. 12.
    Kloesgen, W., Zytkow, J. (eds.): Handbook of Knowledge Discovery and Data Mining. Oxford University Press, Oxford (2002)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Andrzej Skowron
    • 1
  • Roman Swiniarski
    • 2
    • 3
  • Piotr Synak
    • 4
  1. 1.Institute of MathematicsWarsaw UniversityWarsawPoland
  2. 2.Institute of Computer SciencePolish Academy of SciencesWarsawPoland
  3. 3.Department of Mathematical and Computer SciencesSan Diego State UniversitySan DiegoUSA
  4. 4.Polish-Japanese Institute of Information TechnologyWarsawPoland

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