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Covering-Based Optimistic-Pessimistic Multigranulation Decision-Theoretic Rough Sets

  • Caihui LiuEmail author
  • Jin Qian
  • Nan Zhang
  • Meizhi Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11103)

Abstract

Multigranulation decision-theoretic rough sets (MDTRS) is a workable model for real-world decision making. The fruitful research achievements of the use of these models have been reported in different aspects. In most existing optimistic MDTRS models, the lower and upper approximations are defined based on the strategy seeking commonality while preserving differences, while pessimistic MDTRS models based on the strategy Seeking commonality while eliminating differences in the definitions of approximations. But in real life, one may need different strategies in defining lower approximation and upper approximation. This paper defines a new MDTRS approach in the frameworks of multi-covering approximation spaces by using different strategies in defining lower and upper approximation, namely, covering-based optimistic-pessimistic multigranulation decision-theoretic rough sets. We first explore a number of basic properties of the new model. Then, we elaborate on the relationship between the proposed models and the existing ones in literature and disclose the interrelationships of the new models.

Keywords

Covering Multigranulation Decision-theoretic rough sets Optimistic Pessimistic 

Notes

Acknowledgements

This work was supported by the China National Natural Science Foundation of Science Foundation under Grant Nos.: 61663002, 61741309, 61403329, 61305052 and Jiangxi Province Natural Science Foundation of China under Grant No.: 20171BAB202034.

References

  1. 1.
    Yao, Y.Y., Wong, S.K.M.: A decision theoretic framework for approximating concepts. Int. J. Man Mach. Stud. 37, 793–809 (1992)CrossRefGoogle Scholar
  2. 2.
    Herbert, J.P., Yao, J.T.: Game-theoretic rough sets. Fundamenta Informaticae 108(3–4), 267–286 (2011)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Liu, D., Li, T.R., Li, H.X.: A multiple-category classification approach with decision-theoretic rough sets. Fundamenta Informaticae 115(2–3), 173–188 (2012)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Yu, H., Liu, Z.G., Wang, G.Y.: An automatic method to determine the number of clusters using decision-theoretic rough set. Int. J. Approx. Reason. 55(1), 101–115 (2014)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Li, T.J., Yang, X.P.: An axiomatic characterization of probabilistic rough sets. Int. J. Approx. Reason. 55(1), 130–141 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Jia, X.Y., Tang, Z.M., Liao, W.H., Shang, L.: On an optimization representation of decision-theoretic rough set model. Int. J. Approx. Reason. 55(1), 156–166 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180, 341–353 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Yao, Y.: An outline of a theory of three-way decisions. In: Yao, J.T., et al. (eds.) RSCTC 2012. LNCS (LNAI), vol. 7413, pp. 1–17. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-32115-3_1CrossRefGoogle Scholar
  9. 9.
    Zhou, B., Yao, Y., Luo, J.: A three-way decision approach to email spam filtering. In: Farzindar, A., Kešelj, V. (eds.) AI 2010. LNCS (LNAI), vol. 6085, pp. 28–39. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-13059-5_6CrossRefGoogle Scholar
  10. 10.
    Li, H.X., Zhang, L.B., Huang, B., Zhou, X.Z.: Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl. Based Syst. 91, 241–251 (2016)CrossRefGoogle Scholar
  11. 11.
    Zhang, H.R., Min, F.: Three-way recommender systems based on random forests. Knowl. Based Syst. 91, 275–286 (2016)CrossRefGoogle Scholar
  12. 12.
    Qian, Y.H., Zhang, H., Sang, Y.L., Liang, J.L.: Multigranulation decision-theoretic rough sets. Int. J. Approx. Reason. 55(1), 225–237 (2014)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Qian, Y.H., Liang, X.Y., Lin, G.P.: Local multigranulation decision-theoretic rough sets. Int. J. Approx. Reason. 82, 119–137 (2017)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Liu, C., Wang, M., Zhang, N.: Covering-based optimistic multigranulation decision-theoretic rough sets based on maximal descriptors. In: Polkowski, L., et al. (eds.) IJCRS 2017. LNCS (LNAI), vol. 10314, pp. 238–248. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-60840-2_17CrossRefGoogle Scholar
  15. 15.
    Liu, C., Wang, M.: Optimistic decision-theoretic rough sets in multi-covering space. In: Flores, V., et al. (eds.) IJCRS 2016. LNCS (LNAI), vol. 9920, pp. 282–293. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-47160-0_26CrossRefGoogle Scholar
  16. 16.
    Qian, J.: Research on multigranulation decision-theoretic rough set models. J. Zhengzhou Univ. (Nat. Sci. Edn.).  https://doi.org/10.13705/j.issn.1671-6841.2017069. (in Chinese with English Abstract)
  17. 17.
    Zakowski, W.: Approximations in the space \((U,\varPi )\). Demonstratio Mathematica 16, 761–769 (1983)MathSciNetCrossRefGoogle Scholar
  18. 18.
    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
  19. 19.
    Zhu, W., Wang, F.Y.: On three types of covering rough sets. IEEE Trans. Knowl. Data Eng. 19, 1131–1144 (2007)CrossRefGoogle Scholar
  20. 20.
    Gong, Z.T., Shi, Z.H.: On the covering probabilistic rough set models and its Bayes desicions. Fuzzy Syst. Math. 22(4), 142–148 (2008). (Chinese with English abstract)Google Scholar
  21. 21.
    Liu, C.H., Miao, D.Q., Qian, J.: On multi-granulation covering rough sets. Int. J. Approx. Reason. 55, 1404–1418 (2014)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Li, H.X., Zhang, L.B., Zhou, X.Z., Huang, B.: Cost-sensitive sequential three-way decision modeling using a deep neural network. Int. J. Approx. Reason. 85, 68–78 (2017)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Feng, T., Fan, H.T., Mi, J.S.: Uncertainty and reduction of variable precision multigranulation fuzzy rough sets based on three-way decisions. Int. J. Approx. Reason. 85, 36–58 (2017)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Sun, B.Z., Ma, W.M., Xiao, X.: Three-way group decision making based on multigranulation fuzzy decision-theoretic rough set over two universes. Int. J. Approx. Reason. 81, 87–102 (2017)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Qian, Y.H., Liang, X.Y., Lin, G.P., Qian, G., Liang, J.Y.: Local multigranulation decision-theoretic rough sets. Int. J. Approx. Reason. 82, 119–137 (2017)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Ju, H.R., Li, H.X., Yang, X.B., Zhou, X.Z., Huang, B.: Cost-sensitive rough set: a multi-granulation approach. Knowl. Based Syst. 123, 137–153 (2017).  https://doi.org/10.1016/j.knosys.2017.02.019CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceGannan Normal UniversityGanzhouChina
  2. 2.College of Computer EngineeringJiangsu University of TechnologyChangzhouChina
  3. 3.School of Computer and Control EngineeringYantai UniversityYantaiChina
  4. 4.Department of Physical EducationGannan Normal UniversityGanzhouChina

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