Advertisement

Rough Set Theory from a Math-Assistant Perspective

  • Adam Grabowski
  • Magdalena Jastrzȩbska
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4585)

Abstract

In the paper, we draw a perspective of the computer-assisted theory exploration within rough set theory. We examine two well-known approaches to the topic, drawing some paradigms for a machine math-assistant to be feasible tool any researcher can use to verify his own results. Some features of a Mizar language chosen for the verification task are also presented.

Keywords

Approximation Space Jordan Curve Theorem Indiscernibility Relation Mizar Mathematical Library Contact Algebra 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bryniarski, E.: Formal conception of rough sets. Fundamenta Informaticae 27(2-3), 109–136 (1996)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Düntsch, I., Winter, M.: Construction of Boolean contact algebras. AI Communications 13, 235–246 (2004)Google Scholar
  3. 3.
    Gomolińska, A.: A comparative study of some generalized rough approximations. Fundamenta Informaticae 51(1-2), 103–119 (2002)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Grabowski, A.: On the computer-assisted reasoning about rough sets. In: Dunin-Kȩplicz, B., et al. (eds.) Monitoring, Security, and Rescue Techniques in Multiagent Systems. Advances in Soft Computing, pp. 215–226. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Grabowski, A., Schwarzweller, C.: Rough Concept Analysis – theory development in the Mizar system. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 130–144. Springer, Heidelberg (2004)Google Scholar
  6. 6.
    Iwiński, T.B.: Algebraic approach to rough sets. Bull. Pol. Acad. Sci. Math. 35, 673–683 (1987)zbMATHGoogle Scholar
  7. 7.
    Järvinen, J.: Approximations and rough sets based on tolerances. In: Ziarko, W., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 182–189. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  8. 8.
    Järvinen, J.: Ordered set of rough sets. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 49–58. Springer, Heidelberg (2004)Google Scholar
  9. 9.
    Pawlak, Z.: Rough Sets. International Journal of Information and Computer Science 11, 341–356 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Pomykała, J.A.: About tolerance and similarity relations in information systems. In: Alpigini, J.J., Peters, J.F., Skowron, A., Zhong, N. (eds.) RSCTC 2002. LNCS (LNAI), vol. 2475, pp. 175–182. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  11. 11.
    Skowron, A., Stepaniuk, J.: Tolerance approximation spaces. Fundamenta Informaticae 27(2-3), 245–253 (1996)zbMATHMathSciNetGoogle Scholar
  12. 12.
    Yao, Y.Y.: Two views of the theory of rough sets in finite universes. International Journal of Approximation Reasoning 15(4), 291–317 (1996)zbMATHCrossRefGoogle Scholar
  13. 13.
    Ziarko, W.: Variable precision rough set model. Journal of Computer and System Sciences 46(1), 39–59 (1993)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Adam Grabowski
    • 1
  • Magdalena Jastrzȩbska
    • 1
  1. 1.Institute of Mathematics, University of Białystok, ul. Akademicka 2, 15-267 BiałystokPoland

Personalised recommendations