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Extension of Covering Approximation Space and Its Application in Attribute Reduction

  • Guoyin Wang
  • Jun Hu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6401)

Abstract

The concept of the complement of a covering is introduced firstly, and then the complement space and extended space of a covering approximation space is defined based on it. It is proved that a covering approximation space will generate the same covering lower and upper approximations as its complement space and extended space if the covering is degenerated to a partition. Moreover, the extended space of a covering approximation space often generate a bigger covering lower approximation or smaller covering upper approximation than itself. Through extending each covering in a covering decision system, the classification ability of each covering is improved. Thus, a heuristic reduction algorithm is developed to eliminate some coverings in a covering decision system without decreasing the classification ability of the system for decision. Theoretic analysis and example illustration indicate that this algorithm can get shorter reduction than other algorithms.

Keywords

covering rough set covering decision system attribute reduction 

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References

  1. 1.
    Pawlak, Z.: Rough set. International Journal of Computer and Information Sciences 11, 341–356 (1982)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Kryszkiewicz, M.: Rough set approach to incomplete information systems. Information Science 112, 39–49 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Slowinski, R., Vsnderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Tansactions on Knowledge and Data Engineering 12, 331–326 (2000)Google Scholar
  4. 4.
    Wang, G.Y.: Extension of rough set under incomplete information systems. Journal of Computer Research and Development 39, 1238–1243 (2002)Google Scholar
  5. 5.
    Zhu, W.: Generalized rough sets based on relations. Information Sciences 177, 4997–5011 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Zakowski, W.: Approximation in the space (U, Π). Demonstratio Mathematica 16, 761–769 (1983)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Bonikowski, Z., Bryniarski, E., Wybraniec, U.: Extensions and intentions in the rough set theory. Information Sciences 107, 149–167 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Tsang, E.C.C., Chen, D.G., Lee, J.W.T., Yeung, D.S.: On the upper approximations of covering generalized rough sets. In: 3rd International Conference Machine Learning and Cybermetics, Shanghai, China, pp. 4200–4203 (2004)Google Scholar
  9. 9.
    Zhu, W., Wang, F.Y.: A new type of covering rough set. In: 3rd International IEEE Conference Intelligent Systems, London, pp. 444–449 (2006)Google Scholar
  10. 10.
    Zhu, W.: Topological approaches to covering rough sets. Information Sciences 177, 1499–1508 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Zhu, W., Wang, F.Y.: On Three Types of Covering-Based Rough Sets. IEEE Transactions on Knowledge and Data Engineering 19, 1131–1144 (2007)CrossRefGoogle Scholar
  12. 12.
    Zhu, W., Wang, F.Y.: Reduction and axiomization of covering generalized rough sets. Information Sciences 152, 217–230 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Hu, J., Wang, G.Y.: knowledge reduction of covering approximation space. Transction on Computer Science 5540, 69–80 (2009)CrossRefGoogle Scholar
  14. 14.
    Huang, B., He, X., Zhou, X.Z.: Rough entropy based on generalized rough sets covering reduction. Journal of Software 15, 215–220 (2004)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Xu, W.H., Zhang, W.X.: Measuring roughness of generalized rough sets induced by a covering. Fuzzy sets and systems 158, 2443–2455 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Wang, G.Y.: Rough set theory and knowledge acquisition. Xi’an Jiaotong University Press, Xi’an (2001)Google Scholar
  17. 17.
    Chen, D.G., Wang, C.Z., Hu, Q.H.: A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Information Sciences 177, 3500–3518 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Li, F., Yin, Y.Q.: Approaches to knowledge reduction of covering decision systems based on information theory. Information Sciences 179, 1694–1704 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Information Sciences 179, 210–225 (2009)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Guoyin Wang
    • 1
  • Jun Hu
    • 1
    • 2
  1. 1.Institute of Computer Science and TechnologyChongqing University of Posts and TelecommunicationsChongqingP.R. China
  2. 2.School of Electronic EngineeringXiDian UniversityXi’an, ShaanxiP.R. China

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