Advertisement

Knowledge Spaces and Reduction of Covering Approximation Spaces

  • Tong-Jun LiEmail author
  • Shen-Ming Gu
  • Wei-Zhi Wu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9436)

Abstract

Theory of covering rough sets is one kind of effective methods for knowledge discovery. In Bonikowski covering approximation spaces, all definable sets on the universe form a knowledge space. This paper focuses on the theoretic study of knowledge spaces of covering approximation spaces. One kind of dependence relations among covering approximation spaces is introduced, the relationship between the dependence relation and lower and upper covering approximation operators are discussed in detail, and knowledge spaces of covering approximation spaces are well characterized by them. By exploring the dependence relation between a covering approximation space and its sub-spaces, the notion of the reduction of covering approximation spaces is induced, and the properties of the reductions are investigated.

Keywords

Covering rough sets Knowledge spaces Dependence Reduction 

Notes

Acknowledgements

This work was supported by grants from the National Natural Science Foundation of China (Nos. 11071284, 61075120, 61272021, 61202206) and the Zhejiang Provincial Natural Science Foundation of China (Nos. LY14F030001, LZ12F03002, LY12F02021).

References

  1. 1.
    Bonikowski, Z., Bryniarski, E., Wybraniec, U.: Extensions and intentions in the rough set theory. Inf. Sci. 107, 149–167 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Caspard, N., Monjardet, B.: The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey. Discrete Appl. Math. 127, 241–269 (2003)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Chen, D., Wang, C., Hu, Q.: A new approach to attributes reduction of consistent and inconsistent covering decision systems with covering rough sets. Inf. Sci. 177, 3500–3518 (2007)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Doignon, J.P., Falmagne, J.C.: Knowledge Spaces. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Kortelainen, J.: On the relationship between modified sets, topological spaces and rough sets. Fuzzy Sets Syst. 61, 91–95 (1994)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Liu, C., Miao, D.Q., Qian, J.: On multi-granulation covering rough sets. Int. J. Approx. Reason. 44, 1404–1418 (2015)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Li, T.J., Leung, Y., Zhang, W.X.: Generalized fuzzy rough approximation operators based on fuzzy coverings. Int. J. Approx. Reason. 48, 836–856 (2008)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Restrepo, M., Cornelis, C., Gomez, J.: Partial order relation for approximation operators in covering based rough sets. Inf. Sci. 284, 44–59 (2014)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Monjardet, B.: The presence of lattice theory in discrete problems of mathematical social sciences. Why. Math. Soc. Sci. 46, 103–144 (2003)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)CrossRefGoogle Scholar
  11. 11.
    Qian, Y.H., Liang, J.Y., Pedrycz, W., Dang, C.Y.: Positive approximation: an accelerator for attribute reduction in rough set theory. Artif. Intell. 174, 597–618 (2010)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Slowinski, R., Vanderpooten, D.: A generalized definition of rough approximations based on similarity. IEEE Trans. Knowl. Data Eng. 12, 331–336 (2000)CrossRefGoogle Scholar
  13. 13.
    Wang, L., Yang, X., Yang, J.: Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system. Inf. Sci. 207, 66–78 (2012)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Xu, W.H., Zhang, W.X.: Measuring roughness of generalized rough sets induced by a covering. Fuzzy Sets Syst. 158, 2443–2455 (2007)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Yang, T., Li, Q.: Reduction about approximation spaces of covering generalized rough sets. Int. J. Approx. Reason. 51, 335–345 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yao, Y.Y.: Information granulation and rough set approximation. Int. J. Intell. Syst. 16, 87–104 (2001)CrossRefGoogle Scholar
  17. 17.
    Yao, Y.Y.: The superiority of three-way decisions in probabilistic rough set models. Inf. Sci. 181, 1080–1096 (2011)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Yao, Y., Yao, B.: Covering based rough set approximations. Inf. Sci. 200, 91–107 (2012)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Yue, X.D., Miao, D.Q., Zhang, N., Cao, L.B., Wu, Q.: Multiscale roughness measure for color image segmentation. Inf. Sci. 216, 93–112 (2012)CrossRefGoogle Scholar
  20. 20.
    Zakowski, W.: Approximations in the space \((u,\prod )\). Demonstratio Mathematica 16, 761–769 (1983)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zhang, J.B., Li, T.R., Chen, H.M.: Composite rough sets for dynamic data mining. Inf. Sci. 257, 81–100 (2014)MathSciNetCrossRefGoogle Scholar
  22. 22.
    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) CrossRefGoogle Scholar
  23. 23.
    Zhu, W., Wang, F.Y.: Reduction and axiomization of covering generalized rough sets. Inf. Sci. 152, 217–230 (2003)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Zhu, W., Wang, F.Y.: The fourth type of covering-based rough sets. Inf. Sci. 201, 80–92 (2012)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (http://creativecommons.org/licenses/by-nc/2.5/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Authors and Affiliations

  1. 1.School of Mathematics, Physics and Information ScienceZhejiang Ocean UniversityZhoushanChina
  2. 2.Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang ProvinceZhoushanChina

Personalised recommendations