Skip to main content
SpringerLink
Log in

Multigranulation Rough Set Methods and Applications Based on Neighborhood Dominance Relation in Intuitionistic Fuzzy Datasets

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

With the redundancy and complexity of information and data, how to acquire the samples that meet the requirements is an inevitable task in data analysis. There is a general consensus that the neighborhood rough set (NRS) has become the mainstream method for data mining and knowledge classification. Whereas, the limitations still exist in the neighborhood relation for it cannot more accurately reflect the dominance relations that commonly exist in actual data, nor can it select the required data according to different conditions. Enlightened by this idea, this paper focuses on the intuitionistic fuzzy neighborhood dominance relation, which both refines the relationship between samples in the neighborhood and mines the needed samples in data analysis. On this basis, we define the neighborhood dominance rough set (NDRS) model in intuitionistic fuzzy ordered information system (IFOIS). Moreover, we establish the multigranulation neighborhood dominance rough set (MNDRS) from multiple perspectives, and discuss related properties between NDRS and MNDRS. Meanwhile, we compare the NDRS with other rough set models from the roughness and the dependence degree viewpoints. Finally, we adopt nine UCI data sets and implement a series of experiments to illustrate the feasibility and effectiveness of the proposed models.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bing, H.: A dominance interval-valued intuitionistic fuzzy-rough set model and its application. J. Nanjing Univ. (Nat. Sci.) 48(4), 367–375 (2012)

    MathSciNet  MATH  Google Scholar 

  3. Bing, H., Li, H.X., Wei, D.K.: Dominance-based rough set model in intuitionistic fuzzy information systems. Knowl. Based Syst. 28(28), 115–123 (2013)

    Google Scholar 

  4. Cha, B., Li, Z.: A dynamic framework for updating neighborhood multigranulation approximations with the variation of objects. Inf. Sci. 519, 82–406 (2020)

    MathSciNet  Google Scholar 

  5. Chen, W., Yang, X., Yang, J., et al.: Dominance-based rough set approach and knowledge reductions in incomplete ordered information system. Inf. Sci. Int. J. 178(4), 1219–1234 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen, H.M., Li, T.R., Luo, C. et al.: Dominance-Based Neighborhood Rough Sets and Its Attribute Reduction, pp. 89–99. Springer, Cham (2015)

  7. Chen, H.M., Cai, Y., Li, T.R., et al.: Parallel attribute reduction in dominance-based neighborhood rough set. Inf. Sci. 373, 351–368 (2016)

    Article  MATH  Google Scholar 

  8. Chen, H.M., Li, T.R., Sang, B.B., Xu, W.H., Yu, H.: Incremental approaches for heterogeneous feature selection in dynamic ordered data. Inf. Sci. 541, 475–501 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chen, X.W., Xu, W.H.: Double-quantitative multigranulation rough fuzzy set based on logical operations in multi-source decision systems. Int. J. Mach. Learn. Cybern. (2022). https://doi.org/10.1007/s13042-021-01433-2

    Article  Google Scholar 

  10. Ding, W., Sun, L., Wang, L., et al.: Feature selection using fuzzy neighborhood entropy-based uncertainty measures for fuzzy neighborhood multigranulation rough sets. IEEE Trans. Fuzzy Syst. 99, 19–33 (2020)

    Google Scholar 

  11. Du, W.S., Hu, B.Q.: Dominance-based rough set approach to incomplete ordered information systems. Inf. Sci. 346, 106–129 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Greco, S., Matarazzo, B., Slowinski, R.: Rough approximation of a preference relation by dominance relations. Eur. J. Oper. Res. 117, 63–83 (1999)

    Article  MATH  Google Scholar 

  13. Greco, S., Matarazzo, B., Slowinski, R.: Rough approximation by dominance relations. Int. J. Intell. Syst. 17(2), 153–171 (2002)

    Article  MATH  Google Scholar 

  14. Guo, C.X., Huang, B., Zhuang, Y.L., et al.: Intuitionistic fuzzy multigranulation rough sets. Inf. Sci. 277, 299–320 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Guo, Y.T., Xu, W.H.: Generalized multigranulation double-quantitative decision-theoretic rough set. Knowl. Based Syst. 105(1), 190–205 (2016)

    Google Scholar 

  16. Hu, Q., Liu, J., Wu, C., Yu, D.: Neighborhood rough set based heterogeneous feature subset selection. Inf. Sci. 178(18), 3577–3594 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  17. Hua, J.X., Lu, Y.L., Lei, Y.J.: Attribute reduction based on intuitionistic fuzzy rough set. Control Decis. 24(3), 335–341 (2009)

    MathSciNet  Google Scholar 

  18. Huang, B., Wei, D.K.: Distance-based rough set model in intuitionistic fuzzy information systems and its application. Syst. Eng. Theory Pract. 31, 1357–1362 (2011)

  19. Huang, B., Li, H., Wei, D.: Using a rough set model to extract rules in dominance-based interval-valued intuitionistic fuzzy information systems. Inf. Sci. 221, 215–229 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  20. Huang, B., Li, H.X., Zhuang, Y.L., et al.: A dominance intuitionistic fuzzy-rough set approach and its applications. Appl. Math. Model. 37, 7128–7141 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  21. Huang, B., Guo, C.X., Zhuang, Y.L.: Intuitionistic fuzzy multigranulation rough sets. Inf. Sci. 277, 299–320 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Huang, B., Li, H., Zhang, L., Zhou, X.: Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl. Based Syst. 91, 241–251 (2016)

    Article  Google Scholar 

  23. Inbarani, H.H.: A novel neighborhood rough set based classification approach for medical diagnosis. Procedia Comput. Sci. 47, 351–359 (2015)

    Article  Google Scholar 

  24. Kong, Q., Xu, W.H.: The comparative study of covering rough sets and multi-granulation rough sets, Soft Comput. 23, 3237–3251 (2019)

  25. Li, W.T., Xu, W.H., Zhang, X.Y., Zhang, J.: Updating approximations with dynamic objects based on local multigranulation rough sets in ordered information systems. Artif. Intell. Rev. (2021). https://doi.org/10.1007/s10462-021-10053-9

  26. Liang, J.Y., Qian, Y.H., Yao, Y.Y., et al.: MGRS: a multi-granulation rough set. Inf. Sci. 180(6), 949–970 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  27. Liang, D.C., Liu, D., Xu, Z.S.: Three-way decisions with intuitionistic fuzzy decision-theoretic rough sets based on point operators. Inf. Sci. 375, 183–201 (2017)

    Article  MATH  Google Scholar 

  28. Liang, X.Y., Qian, Y.H., Wang, Q., et al.: Local neighborhood rough set. Knowl. Based Syst. 153, 53–64 (2018)

    Article  Google Scholar 

  29. Mandal, P., Ranadive, A.S.: Fuzzy multigranulation decision-theoretic rough sets based on fuzzy preference relation. Soft Comput. 23(1), 85–99 (2019)

    Article  MATH  Google Scholar 

  30. Pawlak, Z.: Rough set. Int. J. Comput. Inf. Sci. 11(5), 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  31. Song, Q., Chissom, B.S.: Fuzzy time-series and its models. Fuzzy. Set. Sys. 54(3), 269–277 (1993)

  32. Skowron, A., Stepaniuk, J.: Tolerance approximation space. Fundam. Inf. 27, 245–253 (1996)

    MATH  Google Scholar 

  33. Skowron, A., Stepaniuk, J.: Information Granules and Rough Neural Computing, pp. 43–84. Springer, Berlin (2004)

    Book  Google Scholar 

  34. Wang, Q., Xu, W.H., Zhang, X.Y.: A generalized multi-granulation rough set approach. In: Bio-Inspired Computing and Applications—7th International Conference on Intelligent Computing, ICIC 2011, Zhengzhou,China, 11–14 August 2011, Revised Selected Papers. Springer, Berlin (2011)

  35. Wang, Q.R., Xu, W.H., Zhang, X.T.: Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space. Int. J. Fuzzy Syst. 13, 246–259 (2011)

    MathSciNet  Google Scholar 

  36. Wu, W.Z., Zhang, W.X.: Neighborhood operator systems and approximations. Inf. Sci. 144, 201–217 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  37. Xu, W.H., Guo, Y.T.: Generalized multigranulation double-quantitative decision-theoretic rough set. Knowl. Based Syst. 105(1), 190–205 (2016)

    Article  Google Scholar 

  38. Xu, W.H., Li, W.T.: Granular computing approach to two-way learning based on formal concept analysis in fuzzy datasets. IEEE Trans. Cybern. 46(2), 366–379 (2016)

    Article  MathSciNet  Google Scholar 

  39. Xu, W.H., Yu, J.H.: Incremental knowledge discovering in interval-valued decision information system with the dynamic data. Int. J. Mach. Learn. Cybern. 8(3), 1–16 (2015)

    Google Scholar 

  40. Xu, W.H., Yu, J.H.: A novel approach to information fusion in multi-source datasets: a granular computing viewpoint. Inf. Sci. 378, 410–423 (2017)

    Article  MATH  Google Scholar 

  41. Xu, W.H., Yuan, K.H., Li, W.T.: Dynamic updating approximations of local generalized multigranulation neighborhood rough set. Appl. Intell. (2022). https://doi.org/10.1007/s10489-021-02861-x

  42. Xu, W.H., Zhang, X.Y., Zhang, W.: Two new types of multiple granulation rough set. ISRN Appl. Math. (2013). https://doi.org/10.1155/2013/791356

  43. Xu, W.H., Zhang, J., Zhang, X.Y.: Attribute reduction in interval-valued fuzzy ordered decision tables via evidence theory. J. Eng. 16, 1475–1482 (2018)

    Google Scholar 

  44. Xu, W.H., Zhang, J., Zhang, X.Y., et al.: Local multigranulation decision-theoretic rough set in ordered information systems. Soft Comput. 23, 13247–13261 (2019)

    Article  MATH  Google Scholar 

  45. Xue, Z., Si, X., Yuan, Y. et al.: Model of multi-granulation neighborhood rough intuitionistic fuzzy sets. Pattern Recogn. &. Artif. Intell. 30(1), 11–20 (2017)

  46. Yang, X.: The models of dominance-based multigranulation rough sets. Data Base Syst. Logic Program. 6840, 657–664 (2011)

    Google Scholar 

  47. Yang, X., Yu, D., Yang, J., et al.: Dominance-based rough set approach to incomplete interval-valued information system. Data Knowl. Eng. 68(11), 1331–1347 (2009)

    Article  Google Scholar 

  48. Yang, X., Yong, Q., Yu, H., et al.: Updating multigranulation rough approximations with increasing of granular structures. Knowl. Based Syst. 64, 59–69 (2014)

    Article  Google Scholar 

  49. Yao, Y.Y.: Relational interpretations of neighborhood operators and rough set approximation operators. Inf. Sci. 101, 239–259 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  50. Yuan, K.H., Xu, W.H., Li, W.T., Ding, W.P.: An incremental learning mechanism for object classification based on progressive fuzzy three-way concept. Inf. Sci. 584(1), 127–147 (2022)

  51. Zhang, X., Chen, D.: Generalized Dominance-Based Rrough Set Model for the Dominance Intuitionistic Fuzzy Information Systems. Springer, Cham (2014)

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. 61976254, 61772002).

Author information

Authors and Affiliations

  1. College of Artificial Intelligence, Southwest University, Chongqing, 400715, People’s Republic of China

    Xiaoyan Zhang, Jianglong Hou & Jirong Li

Authors
  1. Xiaoyan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jianglong Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jirong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoyan Zhang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Hou, J. & Li, J. Multigranulation Rough Set Methods and Applications Based on Neighborhood Dominance Relation in Intuitionistic Fuzzy Datasets. Int. J. Fuzzy Syst. 24, 3602–3625 (2022). https://doi.org/10.1007/s40815-022-01325-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-022-01325-9

Keywords

Search

Navigation