Skip to main content
SpringerLink
Log in

Topological Properties for Approximation Operators in Covering Based Rough Sets

  • Conference paper
  • First Online:
Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9437))

Abstract

We investigate properties of approximation operators being closure and topological closure in a framework of sixteen pairs of dual approximation operators, for the study of covering based rough sets. We extended previous results about approximation operators related with closure operators.

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  1. Abo, E.A.: Rough sets and topological spaces based on similarity. Int. J. Mach. Learn. Cybern. 4, 451–458 (2013)

    Article  Google Scholar 

  2. Bian, X., Wang, P., Yu, Z., Bai, X., Chen, B.: Characterization of coverings for upper approximation operators being closure operators. Inf. Sci. 314, 41–54 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  3. Blyth, T.S.: Lattices and Ordered Algebraic Structures. Springer Universitext, London (2005)

    MATH  Google Scholar 

  4. Bonikowski, Z., Brynarski, E.: Extensions and Intensions in rough set theory. Inform. Sci. 107, 149–167 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hai, Y., Wan-rong, Z.: On the topological properties of generalized rough sets. Inform. Sci. 263(1), 141–152 (2014)

    MathSciNet  MATH  Google Scholar 

  6. Järvinen, J.: Lattice theory for rough sets. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J.W., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. Lncs, vol. 4374, pp. 400–498. Springer, Heidelberg (2007)

    Chapter  MATH  Google Scholar 

  7. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982)

    Article  MATH  Google Scholar 

  8. Pei, Z., Pei, D., Zheng, L.: Topology vs generalized rough sets. Int. J. Approximate Reasoning 52, 231–239 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Pomykala, J.A.: Approximation operations in approximation space. Bull. Acad. Pol. Sci. 35(9–10), 653–662 (1987)

    MathSciNet  MATH  Google Scholar 

  10. Wu, Q., Wang, T., Huan, Y., Li, J.: Topology theory on rough sets. IEEE Trans. Syst. Man Cybern. 38, 68–77 (2008)

    Article  Google Scholar 

  11. Restrepo, M., Cornelis, C., Gómez, J.: Duality, conjugacy and adjointness of approximation operators in covering-based rough sets. Int. J. Approximate Reasoning 55, 469–485 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Restrepo, M., Cornelis, C., Gómez, J.: Partial order relation for approximation operators in covering-based rough sets. Inf. Sci. 284, 44–59 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Tsang, E., Chen, D., Lee J., Yeung, D.S.: On the upper approximations of covering generalized rough sets. In: Proceedings of the 3rd International Conference on Machine Learning and Cybernetics, pp. 4200–4203 (2004)

    Google Scholar 

  14. Wang, L., Yang, X., Yang, J., Wu, C.: Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system. Inf. Sci. 207, 66–78 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  15. Xu, W., Zhang, W.: Measuring roughness of generalized rough sets induced by a covering. Fuzzy Sets Syst. 158, 2443–2455 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  16. Xu, Z., Wang, Q.: On the properties of covering rough sets model. J. Henan Normal Univ. Nat. Sci. 33(1), 130–132 (2005)

    MathSciNet  MATH  Google Scholar 

  17. Xun, G., Xiaole, B., Yun, Z.: Topological characterization of coverings for special covering based upper approximation operators. Inf. Sci. 204, 70–81 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. Yang, T., Li, Q.: Reduction about approximation spaces of covering generalized rough sets. Int. J. Approximate Reasoning 51, 335–345 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  19. Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Inf. Sci. 109, 21–47 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  20. Yao, Y.Y., Yao, B.: Covering based rough sets approximations. Inf. Sci. 200, 91–107 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zakowski, W.: Approximations in the space \((u,\pi )\). Demonstratio Math. 16, 761–769 (1983)

    MathSciNet  MATH  Google Scholar 

  22. Zhang, Y., Li, J., Wu, W.: On axiomatic characterizations of three pairs of covering based approximation operators. Inf. Sci. 180(2), 274–287 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhaowen, L.: Topological structure of generalized rough sets. IEEE Trans. Knowl. Data Eng. 19(8), 1131–1144 (2012)

    Google Scholar 

  24. Zhu, W.: Properties of the first type of covering-based rough sets. In: Proceedings of Sixth IEEE International Conference on Data Mining - Workshops, pp. 407–411 (2006)

    Google Scholar 

  25. Zhu, W.: Properties of the second type of covering-based rough sets. In: Proceedings of the IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology, pp. 494–497 (2006)

    Google Scholar 

  26. Zhu, W.: Basic concepts in covering-based rough sets. In: Proceedings of Third International Conference on Natural Computation, pp. 283–286 (2007)

    Google Scholar 

  27. Zhu, W.: Properties of the third type of covering-based rough sets. In: Proceedings of International Conference on Machine Learning and Cybernetics, pp. 3746–2751 (2007)

    Google Scholar 

  28. Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhu, W., Wang, F.: Reduction and axiomatization of covering generalized rough sets. Inf. Sci. 152, 217–230 (2003)

    Article  MATH  Google Scholar 

  30. Zhu, W., Wang, F.: A new type of covering rough set. In: Proceedings of Third International IEEE Conference on Intelligence Systems, pp. 444–449 (2006)

    Google Scholar 

  31. Zhu, W., Wang, F.: On three types of covering based rough sets. IEEE Trans. Knowl. Data Eng. 19(8), 1131–1144 (2007)

    Article  Google Scholar 

  32. Zhu, W.: Topological approach to covering rough sets. Inf. Sci. 177, 1499–1508 (2007)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidad Militar Nueva Granada, Bogotá, Colombia

    Mauricio Restrepo

  2. Universidad Nacional de Colombia, Bogotá, Colombia

    Jonatan Gómez

Authors
  1. Mauricio Restrepo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jonatan Gómez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mauricio Restrepo .

Editor information

Editors and Affiliations

  1. University of Regina, Regina, SK, Canada

    Yiyu Yao

  2. Tianjin University, Tianjin, China

    Qinghua Hu

  3. Chongqing University of Posts and Telecommunications, Chongqing, China

    Hong Yu

  4. University of Kansas, Lawrence, KS, USA

    Jerzy W. Grzymala-Busse

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Restrepo, M., Gómez, J. (2015). Topological Properties for Approximation Operators in Covering Based Rough Sets. In: Yao, Y., Hu, Q., Yu, H., Grzymala-Busse, J.W. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. Lecture Notes in Computer Science(), vol 9437. Springer, Cham. https://doi.org/10.1007/978-3-319-25783-9_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-25783-9_11

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25782-2

  • Online ISBN: 978-3-319-25783-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation