Stochastic Approach to Rough Set Theory

  • Wojciech Ziarko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4259)


The presentation introduces the basic ideas and investigates the stochastic approach to rough set theory. The major aspects of the stochastic approach to rough set theory to be explored during the presentation are: the probabilistic view of the approximation space, the probabilistic approximations of sets, as expressed via variable precision and Bayesian rough set models, and probabilistic dependencies between sets and multi-valued attributes, as expressed by the absolute certainty gain and expected certainty gain measures, respectively. The measures allow for more comprehensive evaluation of rules computed from data and for computation of attribute reduct, core and significance factors in probabilistic decision tables.


Prior Probability Stochastic Approach Decision Attribute Decision Category Gain Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Pawlak, Z.: Rough sets. Intl. Journal of Computer and Information Science 11, 341–356 (1982)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Pawlak, Z.: Rough sets - Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)MATHGoogle Scholar
  3. 3.
    Ziarko, W.: Variable precision rough sets model. Journal of Computer and Systems Sciences 46(1), 39–59 (1993)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. Intl. Journal of Man-Machine Studies 37, 793–809 (1992)CrossRefGoogle Scholar
  5. 5.
    Wong, S.K.M., Ziarko, W.: Comparison of the probabilistic approximate classification and the fuzzy set model. Intl. Journal for Fuzzy Sets and Systems 21, 357–362 (1986)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Wei, L., Zhang, W.: Probabilistic rough sets characterized by fuzzy sets. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 173–180. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  7. 7.
    Greco, S., Matarazzo, B., Słowiński, R.: Rough Membership and Bayesian Confirmation Measures for Parameterized Rough Sets. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 314–324. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Zhong, N., Dong, J., Ohsuga, S.: Data mining: a probabilistic rough set approach. In: Polkowski, L., Skowron, A. (eds.) Rough Sets and Knowledge Discovery, pp. 127–146. Physica Verlag (1998)Google Scholar
  9. 9.
    Inuiguchi, M., Miyajima, T.: Variable precision rough set approach to multiple decision tables. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 304–313. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  10. 10.
    Muto, Y., Kudo, M.: Discernibility-Based Variable Granularity and Kansei Representations. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS (LNAI), vol. 3641, pp. 692–700. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  11. 11.
    Yao, Y.: Probabilistic approaches to rough sets. Expert Systems 20(5), 287–291 (2003)CrossRefGoogle Scholar
  12. 12.
    Slezak, D., Ziarko, W.: The Investigation of the Bayesian rough set model. Intl. Journal of Approximate Reasoning 40, 81–91 (2005)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Ziarko, W.: Set approximation quality measures in the variable precision rough set model. In: Soft Computing Systems, pp. 442–452. IOS Press, Amsterdam (2001)Google Scholar
  14. 14.
    Ziarko, W.: Probabilistic rough sets. In: Ślęzak, D., Wang, G., Szczuka, M.S., Düntsch, I., Yao, Y. (eds.) RSFDGrC 2005. LNCS, vol. 3641, pp. 283–293. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wojciech Ziarko
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaRegina, SaskatchewanCanada

Personalised recommendations