Advertisement

On the Computer-Assisted Reasoning about Rough Sets

  • Adam Grabowski
Part of the Advances in Soft Computing book series (AINSC, volume 28)

Summary

The paper presents some of the issues concerning a formal description of rough sets. We require the indiscernibility relation to be a tolerance of the carrier, not an equivalence relation, as in the Pawlak’s classical approach. As a tool for formalization we use the Mizar system, which is equipped with the largest formalized library of mathematical facts. This uniform and computer-checked for correctness framework seems to present a satisfactory level of generality and may be used by other systems as well as it is easily readable for humans.

Key words

tolerance approximation spaces formalized mathematics automated reasoning knowledge representation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ch. Benzmüller, M. Jamnik, M. Kerber, V. Sorge, Agent-based mathematical reasoning,Electronic Notes in Theoretical Computer Science, 23(3), 1999.Google Scholar
  2. 2.
    E. Bryniarski, Formal conception of rough sets, Fundamenta Informaticae, 27(2–3), 1996, pp. 109–136.zbMATHMathSciNetGoogle Scholar
  3. 3.
    A. Gomolińska. A comparative study of some generalized rough approximations, Fundamenta Informaticae, 51(1–2), 2002, pp. 103–119.MathSciNetGoogle Scholar
  4. 4.
    A. Grabowski, Basic properties of rough sets and rough membership function, to appear in Formalized Mathematics, 12(1), 2004, available at http://mizar.org/JFM/Vol15/roughs_l. html.Google Scholar
  5. 5.
    A. Grabowski, Robbins algebras vs. Boolean algebras, in Proceedings of Mathematical Knowledge Management Conference, Linz, Austria, 2001, available at http://www.emis.de/proceedings/MKM2001/.Google Scholar
  6. 6.
    J. Järvinen, Approximations and rough sets based on tolerances, in: W. Ziarko, Y. Yao (eds.), Proceedings of RSCTC 2000, LNAI 2005, Springer, 2001, pp. 182–189.Google Scholar
  7. 7.
    R.E. Kent, Rough concept analysis: a synthesis of rough sets and formal concept analysis, Fundamenta Informaticae, 27(2–3), 1996, pp. 169–181.zbMATHMathSciNetGoogle Scholar
  8. 8.
    The Mizar Home Page, http://mizar.org.Google Scholar
  9. 9.
    Z. Pawlak, Rough sets, International Journal of Information and Computer Science, 11(5), 1982, pp. 341–356.zbMATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Z. Pawlak, A. Skowron, Rough membership functions, in: R. R. Yaeger, M. Fedrizzi, and J. Kacprzyk (eds.), Advances in the Dempster-Shafer Theory of Evidence, Wiley, New York, 1994, pp. 251–271.Google Scholar
  11. 11.
    A. Skowron, J. Stepaniuk, Tolerance approximation spaces, Fundamenta Informaticae, 27(2–3), 1996, pp. 245–253.zbMATHMathSciNetGoogle Scholar
  12. 12.
    F. Wiedijk, The de Bruijn factor, http://www.cs.kun. nl/∼freek/factor/.Google Scholar
  13. 13.
    L. Zadeh, Fuzzy sets, Information and Control, 8, 1965, pp. 338–353.zbMATHMathSciNetCrossRefGoogle Scholar
  14. 14.
    W. Ziarko, Variable precision rough sets model, Journal of Computer and System Sciences, 46(1), 1993, pp. 39–59.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Adam Grabowski
    • 1
  1. 1.Institute of MathematicsUniversity of BiałystokBiałystokPoland

Personalised recommendations