Formulation and Simplification of Multi-Granulation Covering Rough Sets

  • Tong-Jun Li
  • Xing-Xing Zhao
  • Wei-Zhi Wu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8537)


The theory of multi-granulation rough sets is one kind of effective methods for knowledge discovery in multiple granular structures. Based on rough sets on a single granular structure, various kinds of multi-granulation rough set models are proposed in the past decades. In this paper, according to two kinds of covering rough sets on single-granulation covering approximation spaces, four types of multi-granulation covering rough set models are defined. Properties of new models are examined in detail, comparison of multi-granulation covering approximation operators is done. Finally, simplification of four types of multi-granulation covering rough sets is investigated.


Rough set Multi-granulation Covering rough set Simplification 


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  1. 1.
    Chen, D.G., Wang, C.Z., Hu, Q.H.: A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Information Sciences 177, 3500–3518 (2007)MathSciNetCrossRefGoogle Scholar
  2. 2.
    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 (LNAI), vol. 4259, pp. 174–182. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Lin, G., Liang, J., Qian, Y.: Multigranulation rough sets: From partition to covering. Information Sciences 241, 101–118 (2013)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Lin, G., Qian, Y., Li, J.: NMGRS: Neighborhood-based multigranulation rough sets. International Journal of Approximate Reasoning 53, 1080–1093 (2012)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Liu, C., Miao, D., Qian, J.: On multi-granulation covering rough sets. International Journal of Approximate Reasoning (2014),
  6. 6.
    Ma, L.W.: On some types of neighborhood-related covering rough sets. International Journal of Approximate Reasoning 53, 901–911 (2012)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Pomykala, J.A.: Approximation Operations in Approximation Space. Bulletin of the Polish Academy of Sciences: Mathematics 35, 653–662 (1987)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Qian, Y.H., Liang, J.Y., Yao, Y.Y., Dang, C.Y.: MGRS: A multi-granulation rough set. Information Sciences 180, 949–970 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Qian, Y.H., Liang, J.Y., Wei, W.: Pessimistic rough decision. In: Second International Workshop on Rough Sets Theory, pp. 440–449 (2010)Google Scholar
  11. 11.
    Qian, Y., Zhang, H., Sang, Y., Liang, J.: Multigranulation decision-theoretic rough sets. International Journal of Approximate Reasoning 55, 225–237 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    She, Y., He, X.: On the structure of the multigranulation rough set model. Knowledge-Based Systems 36, 81–92 (2012)CrossRefGoogle Scholar
  13. 13.
    Yang, X., Dou, H., Yang, J.: Hybrid multigranulation rough sets based on equivalence relation. Computer Science 39, 165–169 (2012) (A Chinese journal)Google Scholar
  14. 14.
    Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. International Journal of Man-machine Studies 37, 793–809 (1992)CrossRefGoogle Scholar
  15. 15.
    Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Information Sciences 101, 239–259 (1998)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yao, Y.Y., Yao, B.: Covering based rough set approximations. Information Sciences 200, 91–107 (2012)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Zakowski, W.: Approximations in the space (U, P). Demonstratio Mathematica IXV, 761–769 (1983)Google Scholar
  18. 18.
    Zhang, M., Tang, Z., Xu, W., Yang, X.: Variable multigranulation rough set model. Pattern Recognition and Artificial Intelligence 25, 709–720 (2012) (A Chinese journal)Google Scholar

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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Tong-Jun Li
    • 1
  • Xing-Xing Zhao
    • 1
  • Wei-Zhi Wu
    • 1
  1. 1.School of Mathematics, Physics and Information ScienceZhejiang Ocean UniversityZhoushanP.R. China

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