Skip to main content
SpringerLink
Log in

Knowledge Reduction of Covering Approximation Space

  • Chapter
Transactions on Computational Science V

Part of the book series: Lecture Notes in Computer Science ((TCOMPUTATSCIE,volume 5540))

Abstract

Knowledge reduction is a key issue in data mining. In order to simplify the covering approximation space and mining rules from it, Zhu proposed a reduction of covering approximation space which does not rely on any prior given concept or decision. Unfortunately, it could only reduce absolutely redundant knowledge. To reduce relatively redundant knowledge with respect to a given concept or decision, the problem of relative reduction is studied in this paper. The condition in which an element of a covering is relatively reducible is discussed. By deleting all relatively reducible elements of a covering approximation space, one can get the relative reduction of the original covering approximation space. Moreover, one can find that the covering lower and upper approximations in the reduced space are the same as in the original covering space. That is to say, it does not decrease the classification ability of a covering approximation space to reduce the relatively reducible elements in it. In addition, combining absolute reduction and relative reduction, an algorithm for knowledge reduction of covering approximation space is developed. It can reduce not only absolutely redundant knowledge, but also relatively redundant knowledge. It is significant for the following-up steps of data mining.

This research is supported by the National Natural Science Foundation of P.R. China (No.60573068, No.60773113), Natural Science Foundation of Chongqing (No.2005BA2003, No.2008BA2017), Natural Science Foundation of Chongqing University of Posts and Telecommunications (A2006-56), and Science & Technology Research Program of the Municipal Education Committee of Chongqing (No.KJ060517).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bonikowski, Z., Bryniarski, E., Wybraniec, U.: Extensions and Intentions in the Rough Set Theory. Information Science 107, 149–167 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Hu, J., Wang, G.Y., Zhang, Q.H.: Uncertainty Measure of Covering Generated Rough Set. In: 2006 IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology (WI-IAT 2006 Workshops) (WI-IATW 2006), pp. 498–504 (2006)

    Google Scholar 

  3. Huang, B., He, X., Zhou, X.Z.: Rough Entropy Based on Generalized Rough Sets Covering Reduction. Journal of Software 15(2), 215–220 (2004) (in Chinese)

    MathSciNet  MATH  Google Scholar 

  4. Huang, H., Wang, G.Y., Wu, Y.: An approach for Incomplete Information Systems. In: Dasarathy, B.V. (ed.) Data Mining and Knowledge Discovery: Theory, Tools, and Technology VI. Proceedings of SPIE, vol. 5433, pp. 114–121 (2004)

    Google Scholar 

  5. Kryszkiewicz, M.: Rough Set Approach to Incomplete Information System. Information Sciences 112, 39–49 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kryszkiewicz, M.: Rule in Incomplete Information Systems. Information Sciences 113, 271–292 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Li, T.J.: Rough Approximation Operators in Covering Approximation Spaces. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS, vol. 4259, pp. 174–182. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Mordeson, J.N.: Rough Set Theory Applied to (fuzzy) Ideal Theory. Fuzzy Sets and Systems 121, 315–324 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pal, S., Mitra, P.: Case generation using rough sets with fuzzy representation. IEEE Trans. On Knowledge and Data Engineering 16(3), 292–300 (2004)

    Article  Google Scholar 

  10. Pawlak, Z.: Rough Sets. Computer and Information Science 11, 341–356 (1982)

    MATH  Google Scholar 

  11. Slowinski, R., Vanderpooten, D.: A Generalized Definition of Rough Approximations Based on Similarity. IEEE Tansactions on Knowledge and Data Engineering 12(2), 331–336 (2000)

    Article  Google Scholar 

  12. Tsang, E.C.C., Chen, D., Lee, J.W.T., Yeung, D.S.: On The Upper Approximations of Covering Generalized Rough Sets. In: Proceedings of The Third International Conference on Machine Learning and Cybernetics, Shanghai, pp. 4200–4203 (2004)

    Google Scholar 

  13. Wang, G.Y.: Extension of Rough Set under Incomplete Information Systems. In: IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 1098–1103 (2002)

    Google Scholar 

  14. Yang, Y., Wang, G.Y., Chen, P.J., Zhou, J., He, K.: Feature Selection in Audiovisual Emotion Recognition Based on Rough Set Theory. In: Peters, J.F., Skowron, A., Marek, V.W., Orłowska, E., Słowiński, R., Ziarko, W.P. (eds.) Transactions on Rough Sets VII. LNCS, vol. 4400, pp. 283–294. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  15. Yuan, Z., Wu, Y., Wang, G.Y., Li, J.B.: Motion-Information-Based Video Retrieval System Using Rough Pre-classification. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets V. LNCS, vol. 4100, pp. 306–333. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  16. Zadeh, L.A.: Fuzzy Sets. Inform. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

  17. Zakowski, W.: Approximation in The Space (U, Π). Demonstratio Mathematica 16, 761–769 (1983)

    MathSciNet  MATH  Google Scholar 

  18. Zhong, N., Yao, Y., Ohshima, M.: Peculiarity Oriented Multidatabase Mining. IEEE Trans. Knowledge and Data Eng. 15(4), 952–960 (2003)

    Article  Google Scholar 

  19. Zhu, F.: On Covering Generalized Rough Sets, MS thesis, The University of Arizona, Tucson, Arizona, USA (2002)

    Google Scholar 

  20. Zhu, W., Wang, F.Y.: Reduction and Axiomization of Coving Generalized Rough Sets. Information Science 152, 217–230 (2003)

    Article  MATH  Google Scholar 

  21. Zhu, W.: Topological Approaches to Covering Rough Sets. Information sciences 177, 1499–1508 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhu, W., Wang, F.Y.: On Three Types of Covering-based Rough Sets. IEEE transactions on knowledge and data engineering 19(8), 1131–1144 (2007)

    Article  Google Scholar 

  23. Zhu, W., Wang, F.Y.: Covering Based Granular Computing for Conflict Analysis. In: Mehrotra, S., Zeng, D.D., Chen, H., Thuraisingham, B., Wang, F.-Y. (eds.) ISI 2006. LNCS, vol. 3975, pp. 566–571. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  24. Zhu, W., Wang, F.Y.: A new type of covering rough sets. In: IEEE IS 2006, 4-6 September 2006, pp. 444–449 (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electronic Engineering, XiDian University, Xi’an, Shaanxi, 710071, P.R. China

    Jun Hu

  2. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, 400065, P.R. China

    Jun Hu & GuoYin Wang

Authors
  1. Jun Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. GuoYin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Calgary, Department of Computer Science, 2500 University Drive N.W, T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  2. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  3. Theoretical and Empirical Software Engineering Research Centre (TESERC), University of Calgary, 2500 University Drive, NW, T2N 1N4, Calgary, Alberta, Canada

    Yingxu Wang

  4. Department of Computing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Keith C. C. Chan

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hu, J., Wang, G. (2009). Knowledge Reduction of Covering Approximation Space. In: Gavrilova, M.L., Tan, C.J.K., Wang, Y., Chan, K.C.C. (eds) Transactions on Computational Science V. Lecture Notes in Computer Science, vol 5540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02097-1_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02097-1_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02096-4

  • Online ISBN: 978-3-642-02097-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation