Partitions, Coverings, Reducts and Rule Learning in Rough Set Theory

  • Yiyu Yao
  • Rong Fu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6954)


When applying rough set theory to rule learning, one commonly associates equivalence relations or partitions to a complete information table and tolerance relations or coverings to an incomplete table. Such associations are sometimes misleading. We argue that Pawlak three-step approach for data analysis indeed uses both partitions and coverings for a complete information table. A slightly different formulation of Pawlak approach is given based on the notions of attribute reducts of a classification table, attribute reducts of objects and rule reducts. Variations of Pawlak approach are examined.


Attribute reduction coverings partitions rule learning 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Blaszczynski, J., Slowinski, R., Szelag, M.: Sequential covering rule induction algorithm for variable consistency rough set approaches. Information Sciences 181, 987–1002 (2011)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Cendrowska, J.: PRISM: An algorithm for inducing modular rules. International Journal of Man-Machine Studies 27, 349–370 (1987)CrossRefMATHGoogle Scholar
  3. 3.
    Fürnkranz, J.: Separate-and-conquer rule learning. Artificial Intelligence Review 13, 3–54 (1999)CrossRefMATHGoogle Scholar
  4. 4.
    Grzymala-Busse, J.: LERS - A system for learning from examples based on rough sets. In: Slowinski, R. (ed.) Intelligent Decision Support: Handbook of Applications and Advances of the Rough Sets Theory, pp. 3–18. Kluwer Academic Publishers, Dordrecht (1992)CrossRefGoogle Scholar
  5. 5.
    Grzymala-Busse, J., Rzasa, W.: Approximation space and LEM2-like algorithms for computing local coverings. Fundamenta Informaticae 85, 205–217 (2008)MathSciNetMATHGoogle Scholar
  6. 6.
    Mi, J.S., Leung, Y., Wu, W.Z.: Dependence-space-based attribute reduction in consistent decision tables. Soft Computing 15, 261–268 (2011)CrossRefMATHGoogle Scholar
  7. 7.
    Pawlak, Z.: Rough sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)CrossRefMATHGoogle Scholar
  8. 8.
    Pawlak, Z., Skowron, A.: Rough sets and Boolean reasoning. Information Sciences 177, 41–73 (2007)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Quinlin, J.R.: Induction of decision tree. Machine Learning 1, 81–106 (1986)Google Scholar
  10. 10.
    Van Mechelen, I., Hampton, J., Michalski, R.S., Theuns, P. (eds.): Categories and Concepts: Theoretical Views and Inductive Data Analysis. Academic Press, New York (1993)Google Scholar
  11. 11.
    Yao, Y.Y.: Interpreting concept learning in cognitive informatics and granular computing. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics 39, 855–866 (2009)CrossRefGoogle Scholar
  12. 12.
    Yao, Y.Y., Deng, X.F.: A granular computing paradigm for concept learning (2011) (manuscript)Google Scholar
  13. 13.
    Yao, Y., Zhao, Y., Wang, J.: On reduct construction algorithms. In: Wang, G.-Y., Peters, J.F., Skowron, A., Yao, Y. (eds.) RSKT 2006. LNCS (LNAI), vol. 4062, pp. 297–304. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Zhao, Y., Yao, Y.Y., Yao, J.T.: Level construction of decision trees for classification. International Journal Software Engineering and Knowledge Engineering 16, 103–126 (2006)CrossRefGoogle Scholar
  15. 15.
    Zhu, W., Wang, F.Y.: Reduction and axiomization of covering generalized rough sets. Information Sciences 152, 217–230 (2003)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yiyu Yao
    • 1
  • Rong Fu
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada

Personalised recommendations