Knowledge Spaces and Reduction of Covering Approximation Spaces

Conference paper
First Online:
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 
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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)MATHCrossRefGoogle 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)MATHMathSciNetCrossRefGoogle 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)MATHCrossRefGoogle Scholar
  4. 4.
    Doignon, J.P., Falmagne, J.C.: Knowledge Spaces. Springer, Heidelberg (1999)MATHCrossRefGoogle Scholar
  5. 5.
    Kortelainen, J.: On the relationship between modified sets, topological spaces and rough sets. Fuzzy Sets Syst. 61, 91–95 (1994)MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Liu, C., Miao, D.Q., Qian, J.: On multi-granulation covering rough sets. Int. J. Approx. Reason. 44, 1404–1418 (2015)MathSciNetGoogle 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)MATHMathSciNetCrossRefGoogle 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)MATHMathSciNetCrossRefGoogle Scholar
  10. 10.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inf. Sci. 11, 341–356 (1982)MATHMathSciNetCrossRefGoogle 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)MATHMathSciNetCrossRefGoogle 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)MATHCrossRefGoogle 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)MATHCrossRefGoogle Scholar
  15. 15.
    Yang, T., Li, Q.: Reduction about approximation spaces of covering generalized rough sets. Int. J. Approx. Reason. 51, 335–345 (2010)MATHCrossRefGoogle Scholar
  16. 16.
    Yao, Y.Y.: Information granulation and rough set approximation. Int. J. Intell. Syst. 16, 87–104 (2001)MATHCrossRefGoogle Scholar
  17. 17.
    Yao, Y.Y.: The superiority of three-way decisions in probabilistic rough set models. Inf. Sci. 181, 1080–1096 (2011)MATHCrossRefGoogle Scholar
  18. 18.
    Yao, Y., Yao, B.: Covering based rough set approximations. Inf. Sci. 200, 91–107 (2012)MATHCrossRefGoogle 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)MATHMathSciNetGoogle 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)MATHCrossRefGoogle Scholar
  24. 24.
    Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)MATHCrossRefGoogle Scholar
  25. 25.
    Zhu, W., Wang, F.Y.: The fourth type of covering-based rough sets. Inf. Sci. 201, 80–92 (2012)MATHCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

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

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