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Topological Properties for Approximation Operators in Covering Based Rough Sets

  • Mauricio Restrepo
  • Jonatan Gómez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Covering rough sets Approximation operators Topological closure 

References

  1. 1.
    Abo, E.A.: Rough sets and topological spaces based on similarity. Int. J. Mach. Learn. Cybern. 4, 451–458 (2013)CrossRefGoogle Scholar
  2. 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)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Blyth, T.S.: Lattices and Ordered Algebraic Structures. Springer Universitext, London (2005)zbMATHGoogle Scholar
  4. 4.
    Bonikowski, Z., Brynarski, E.: Extensions and Intensions in rough set theory. Inform. Sci. 107, 149–167 (1998)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Hai, Y., Wan-rong, Z.: On the topological properties of generalized rough sets. Inform. Sci. 263(1), 141–152 (2014)MathSciNetzbMATHGoogle Scholar
  6. 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) CrossRefGoogle Scholar
  7. 7.
    Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11(5), 341–356 (1982)CrossRefGoogle Scholar
  8. 8.
    Pei, Z., Pei, D., Zheng, L.: Topology vs generalized rough sets. Int. J. Approximate Reasoning 52, 231–239 (2011)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Pomykala, J.A.: Approximation operations in approximation space. Bull. Acad. Pol. Sci. 35(9–10), 653–662 (1987)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Wu, Q., Wang, T., Huan, Y., Li, J.: Topology theory on rough sets. IEEE Trans. Syst. Man Cybern. 38, 68–77 (2008)CrossRefGoogle Scholar
  11. 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)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Restrepo, M., Cornelis, C., Gómez, J.: Partial order relation for approximation operators in covering-based rough sets. Inf. Sci. 284, 44–59 (2014)MathSciNetCrossRefGoogle Scholar
  13. 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. 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)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Xu, W., Zhang, W.: Measuring roughness of generalized rough sets induced by a covering. Fuzzy Sets Syst. 158, 2443–2455 (2007)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Xu, Z., Wang, Q.: On the properties of covering rough sets model. J. Henan Normal Univ. Nat. Sci. 33(1), 130–132 (2005)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Xun, G., Xiaole, B., Yun, Z.: Topological characterization of coverings for special covering based upper approximation operators. Inf. Sci. 204, 70–81 (2012)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Yang, T., Li, Q.: Reduction about approximation spaces of covering generalized rough sets. Int. J. Approximate Reasoning 51, 335–345 (2010)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Yao, Y.Y.: Constructive and algebraic methods of the theory of rough sets. Inf. Sci. 109, 21–47 (1998)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Yao, Y.Y., Yao, B.: Covering based rough sets approximations. Inf. Sci. 200, 91–107 (2012)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Zakowski, W.: Approximations in the space \((u,\pi )\). Demonstratio Math. 16, 761–769 (1983)MathSciNetzbMATHGoogle Scholar
  22. 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)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Zhaowen, L.: Topological structure of generalized rough sets. IEEE Trans. Knowl. Data Eng. 19(8), 1131–1144 (2012)Google Scholar
  24. 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. 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. 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. 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. 28.
    Zhu, W.: Relationship between generalized rough sets based on binary relation and covering. Inf. Sci. 179, 210–225 (2009)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Zhu, W., Wang, F.: Reduction and axiomatization of covering generalized rough sets. Inf. Sci. 152, 217–230 (2003)CrossRefGoogle Scholar
  30. 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. 31.
    Zhu, W., Wang, F.: On three types of covering based rough sets. IEEE Trans. Knowl. Data Eng. 19(8), 1131–1144 (2007)CrossRefGoogle Scholar
  32. 32.
    Zhu, W.: Topological approach to covering rough sets. Inf. Sci. 177, 1499–1508 (2007)CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2015

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Authors and Affiliations

  1. 1.Universidad Militar Nueva GranadaBogotáColombia
  2. 2.Universidad Nacional de ColombiaBogotáColombia

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