Variable Precision Multigranulation Rough Set and Attributes Reduction

  • Hengrong Ju
  • Xibei YangEmail author
  • Huili Dou
  • Jingjing Song
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8449)


Multigranulation rough set is a new expansion of the classical rough set since the former uses a family of the binary relations instead of single one for the constructing of approximations. In this paper, the model of the variable precision rough set is introduced into the multigranulation environment and then the concept of the variable precision multigranulation rough set is proposed, which include optimistic and pessimistic cases. Not only basic properties of variable precision multigranulation rough set are investigated, but also the relationships among variable precision rough set, multigranulation rough set and variable precision multigranulation rough set are examined. Finally, a heuristic algorithm is presented for computing reducts of variable precision multigranulation rough set, it is also tested on five UCI data sets.


Attributes reduction Multigranulation rough set Variable precision multigranulation rough set 



This work is supported by the Natural Science Foundation of China (Nos. 61100116, 61272419, 61305058), the Natural Science Foundation of Jiangsu Province of China (Nos. BK2011492, BK2012700, BK20130471), Qing Lan Project of Jiangsu Province of China, Key Laboratory of Intelligent Perception and Systems for High-Dimensional Information (Nanjing University of Science and Technology), Ministry of Education (No. 30920130122005), Key Laboratory of Artificial Intelligence of Sichuan Province (No. 2013RYJ03), Natural Science Foundation of Jiangsu Higher Education Institutions of China (Nos. 13KJB520003, 13KJD520008), Postgraduate Innovation Foundation of University in Jiangsu Province of China under Grant No. CXLX13_707.


  1. 1.
    Pawlak, Z.: Rough Sets Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dordrecht (1991)zbMATHGoogle Scholar
  2. 2.
    Ziarko, W.: Variable precision rough set model. J. Comput. Syst. Sci. 46, 39–59 (1993)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ziarko, W.: Probabilistic approach to rough sets. Int. J. Approx. Reason. 49, 272–284 (2008)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Qian, Y.H., Liang, J.Y., Yao, Y.Y., Dang, C.Y.: MGRS: a multi-granulation rough set. Inf. Sci. 180, 949–970 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Qian, Y.H., Liang, J.Y., Dang, C.Y.: Incomplete multigranulation rough set. IEEE Trans. Syst. Man Cybern. 40(2), 420–431 (2010)CrossRefGoogle Scholar
  6. 6.
    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
  7. 7.
    Qian, Y.H., Liang, J.Y., Witold, P., Dang, C.Y.: Positive approximation: an accelerator for attribute reduction in rough set theory. Artif. Intell. 174, 597–618 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Yang, X.B., Qi, Y.S., Song, X.N., Yang, J.Y.: Test cost sensitive multigranulation rough set: model and minimal cost selection. Inf. Sci. 250, 184–199 (2013)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Yang, X.B., Zhang, Y.Q., Yang, J.Y.: Local and global measurements of MGRS rules. Int. J. Comput. Intell. Syst. 5(6), 1010–1024 (2012)CrossRefGoogle Scholar
  10. 10.
    Xu, W.H., Wang, Q.R., Zhang, X.T.: Multi-granulation fuzzy rough set in a fuzzy tolerance approximation space. Int. J. Fuzzy Syst. 13, 246–259 (2011)MathSciNetGoogle Scholar
  11. 11.
    Yang, X.B., Song, X.N., Chen, Z.H., Yang, J.Y.: On multigranulation rough sets in incomplete information system. Int. J. Mach. Learn. Cybern. 3, 223–232 (2012)CrossRefGoogle Scholar
  12. 12.
    Yang, X.B., Song, X.N., Dou, H.L., Yang, J.Y.: Multi-granulation rough set: from crisp to fuzzy case. Ann. Fuzzy Math. Inf. 1, 55–70 (2011)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Yang, X.B., Yang, J.Y.: Incomplete Information System and Rough Set Theory: Models and Attribute Reductions. Science Press & Springer, Beijing and Heidelberg (2012)CrossRefGoogle Scholar
  14. 14.
    Qian, Y.H., Zhang, H., Sang, Y.L., Liang, J.Y.: Multigranulation decision-theoretic rough sets. Int. J. Approx. Reason. 55, 225–237 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lin, G.P., Qian, Y.H., Li, J.J.: NMGRS: Neighborhood-based multigranulation rough sets. Int. J. Approx. Reason. 53, 1080–1093 (2012)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Xu, W., Zhang, X., Wang, Q.: A generalized multi-granulation rough set approach. In: Huang, D.-S., Gan, Y., Premaratne, P., Han, K. (eds.) ICIC 2011. LNCS (LNBI), vol. 6840, pp. 681–689. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  17. 17.
    Dai, J.H., Wang, W.T., Xu, Q.: An uncertainty measure for incomplete decision tables and its applications. IEEE Trans. Cybern. 43(4), 1277–1289 (2013)CrossRefGoogle Scholar
  18. 18.
    Dai, J.H., Wang, W.T., Tian, H.W., Liu, L.: Attribute selection based on a new conditional entropy for incomplete decision systems. Knowl. Based Syst. 39, 207–213 (2013)CrossRefGoogle Scholar
  19. 19.
    Dai, J.H., Tian, H.W., Wang, W.T., Liu, L.: Decision rule mining using classification consistency rate. Knowl. Based Syst. 43, 95–102 (2013)CrossRefGoogle Scholar
  20. 20.
    Dai, J.H.: Rough set approach to incomplete numerical data. Inf. Sci. 241, 43–57 (2013)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Wei, L., Li, H.R., Zhang, W.X.: Knowledge reduction based on the equivalence relations defined on attribute set and its power set. Inf. Sci. 177, 3178–3185 (2007)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Hengrong Ju
    • 1
    • 2
  • Xibei Yang
    • 1
    • 3
    • 4
    Email author
  • Huili Dou
    • 1
    • 2
  • Jingjing Song
    • 1
    • 2
  1. 1.School of Computer Science and EngineeringJiangsu University of Science and TechnologyZhenjiangPeople’s Republic of China
  2. 2.Key Laboratory of Intelligent Perception and Systems for High-Dimensional InformationNanjing University of Science and Technology, Ministry of EducationNanjingPeople’s Republic of China
  3. 3.Artificial Intelligence Key Laboratory of Sichuan ProvinceZigongPeople’s Republic of China
  4. 4.School of Economics and ManagementNanjing University of Science and TechnologyNanjingPeople’s Republic of China

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