Skip to main content
SpringerLink
Log in

A multigranulation rough set model based on variable precision neighborhood and its applications

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

As combinations of neighborhood rough sets and multigranulation rough sets (MRSs), optimistic and pessimistic neighborhood MRSs can handle complex information systems and characterize problems from multiple perspectives. Nevertheless, they require complete inclusion between neighborhood granules and target concepts, which may weaken their fault tolerance. To overcome the challenge, this paper proposes neighborhood MRSs based on variable precision neighborhood (VMRSs), which allow a certain degree of misclassification and noise in data. In VMRSs, we assign different weights to different attribute subsets to distinguish their importance in learning. In addition to investigating the properties of the VMRS model, we focus on the methods of obtaining its required multiple attribute subsets and their weights. Next, we introduce two applications of the VMRS model. One is using it to construct an indicator for evaluating attribute clustering and attribute subset weighting methods. The other is employing it for attribute reduction. Based on distribution distances, we develop a heuristic algorithm framework for obtaining the proposed reducts. The mechanism and applications of VMRSs are explained through a case study on a medical diagnosis issue. Finally, the experiments on real datasets illuminate the effectiveness and superiority of the methods and algorithms in the paper.

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
Algorithm 1
Algorithm 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data Availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Notes

  1. http://archive.ics.uci.edu/ml

References

  1. Ba J, Liu KY, Ju HR, Xu SP, Yang XB (2022) Triple-G: a new MGRS and attribute reduction. Int J Mach Learn Cyb 13(2):337–356

    Google Scholar 

  2. Chen JY, Zhu P (2023) A variable precision multigranulation rough set model and attribute reduction. Soft Comput 27:85–106

    Google Scholar 

  3. Chen Y, Liu KY, Song JJ, Fujita H, Yang XB, Qian YH (2020) Attribute group for attribute reduction. Inform Sci 535:64–80

    MATH  Google Scholar 

  4. Chen Y, Wang PX, Yang XB, Mi JS, Liu D (2021) Granular ball guided selector for attribute reduction. Knowl-Based Syst 229:107326

    Google Scholar 

  5. Demšar J (2006) Statistical comparison of classifiers over multiple data sets. J Mach Learn Res 7:1–30

    MathSciNet  MATH  Google Scholar 

  6. Fujita H, Gaeta A, Loia V, Orciuoli F (2020) Hypotheses Analysis and Assessment in counter-terrorism activities: a method based on OWA and Fuzzy Probabilistic Rough Sets. IEEE T Fuzzy Syst 28(5):831–845

    Google Scholar 

  7. Hu CX, Zhang L (2020) A dynamic framework for updating neighborhood multigranulation approximations with the variation of objects. Inform Sci 519:382–406

    MathSciNet  Google Scholar 

  8. Hu M, Tsang ECC, Guo YT, Chen DG, Xu WH (2021) A novel approach to attribute reduction based on weighted neighborhood rough sets. Knowl-Based Syst 220:106908

    Google Scholar 

  9. Hu QH, Yu DR, Liu JF, Xu CX (2008) Neighborhood rough set based heterogeneous feature subset selection. Inform Sci 178(18):3577–3594

    MathSciNet  MATH  Google Scholar 

  10. Hu QH, Yu DR, Xie ZX (2008) Neighborhood classifiers. Expert Syst Appl 34:866–876

    Google Scholar 

  11. Jaccard P (1912) The distribution of the flora in the alpine zone. New phytologist 11(2):37–50

    Google Scholar 

  12. Kosub S (2019) A note on the triangle inequality for the Jaccard distance. Pattern Recogn Lett 120:36–38

    Google Scholar 

  13. Li JH, Ren Y, Mei CL, Qian YH, Yang XB (2016) A comparative study of multigranulation rough sets and concept lattices via rule acquisition. Knowl-Based Syst 91:152–164

    Google Scholar 

  14. Lin GP, Qian YH, Li JJ (2012) NMGRS: Neighborhood-based multigranulation rough sets. Int J Approx Reason 53(7):1080–1093

    MathSciNet  MATH  Google Scholar 

  15. Liu JH, Lin YJ, Du JX, Zhang HB, Chen ZY, Zhang J (2022) ASFS: A novel streaming feature selection for multi-label data based on neighborhood rough set. Appl Intell: 1–18

  16. Liu KY, Li TR, Yang XB, Yang X, Liu D (2022) Neighborhood rough set based ensemble feature selection with cross-class sample granulation. Appl Soft Comput 131:109747

    Google Scholar 

  17. Liu KY, Li TR, Yang XB, Yang X, Liu D, Zhang PF, Wang J (2022) Granular cabin: An efficient solution to neighborhood learning in big data. Inform Sci 583:189–201

    Google Scholar 

  18. Luo S, Miao DQ, Zhang ZF, Zhang YJ, Hu SD (2020) A neighborhood rough set model with nominal metric embedding. Inform Sci 520:373–388

    MathSciNet  MATH  Google Scholar 

  19. MacQueen J (1967) Some methods for classification and analysis of multivariate observations. Proc fifth Berkeley Symp Mathematical Statistics and Probability 1(14):281–297

    MathSciNet  MATH  Google Scholar 

  20. Mi JS, Wu WZ, Zhang WX (2004) Approaches to knowledge reduction based on variable precision rough set model. Inform Sci 159(3–4):255–272

    MathSciNet  MATH  Google Scholar 

  21. Pawlak Z (1982) Rough sets. Int J Comput Inform Sci 11(5):341–356

  22. Pawlak Z (1991) Rough sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston

    MATH  Google Scholar 

  23. Qian J, Hong CX, Yu Y, Liu CH, Miao DQ (2022) Generalized multigranulation sequential three-way decision models for hierarchical classification. Inform Sci 616:66–87

    Google Scholar 

  24. Qian YH, Cheng HH, Wang JT, Liang JY, Pedrycz W, Dang CY (2017) Grouping granular structures in human granulation intelligence. Inform Sci 382–383:150–169

    Google Scholar 

  25. Qian YH, Li SR, Liang JY, Shi ZZ, Wang F (2014) Pessimistic rough set based decisions: a multigranulation fusion strategy. Inform Sci 264:196–210

    MathSciNet  MATH  Google Scholar 

  26. Qian YH, Liang JY (2006) Rough Set Method Based on Multi-Granulations. 2006 5th IEEE International Conference on Cognitive Informatics. IEEE 1: 297–304

  27. Qian YH, Liang JY, Dang CY (2009) Incomplete multigranulation rough set. IEEE Trans Syst Man Cybern-Part A: Systems and Humans 40(2):420–431

    Google Scholar 

  28. Qian YH, Liang JY, Yao YY, Dang CY (2010) MGRS: a multi-granulation rough set. Inform Sci 180(6):949–970

    MathSciNet  MATH  Google Scholar 

  29. Qian YH, Liang XY, Lin GP, Guo Q, Liang JY (2017) Local multigranulation decision-theoretic rough sets. Int J Approx Reason 82:119–137

    MathSciNet  MATH  Google Scholar 

  30. Robnik-Šikonja M, Kononenko I (2003) Theoretical and empirical analysis of ReliefF and RReliefF. Mach learn 53(1):23–69

    MATH  Google Scholar 

  31. Shu WH, Qian WB, Xie YH (2022) Incremental neighborhood entropy-based feature selection for mixed-type data under the variation of feature set. Appl Intell 52:4792–4806

    Google Scholar 

  32. Sun L, Zhang XY, Qian YH, Xu JC, Zhang SG, Tian Y (2019) Joint neighborhood entropy-based gene selection method with fisher score for tumor classification. Appl Intell 49:1245–1259

    Google Scholar 

  33. Wang CZ, Hu QH, Wang XZ, Chen DG, Qian YH, Dong Z (2018) Feature selection based on neighborhood discrimination index. IEEE Trans Neural Netw Learn Syst 29(7):2986–2999

    MathSciNet  Google Scholar 

  34. Wang CZ, Shao MW, He Q, Qian YH, Qi YL (2016) Feature subset selection based on fuzzy neighborhood rough sets. Knowl-Based Syst 111:173–179

    Google Scholar 

  35. Wang CZ, Shi YP, Fan XD, Shao MW (2019) Attribute reduction based on k-nearest neighborhood rough sets. Int J Approx Reason 106:18–31

    MathSciNet  MATH  Google Scholar 

  36. Wilcoxon F (1945) Individual comparisons by ranking methods. Biometrics 1:80–83

    MathSciNet  Google Scholar 

  37. Wilson DP, Martinez TR (1997) Improved heterogeneous distance functions. J Artif Intell Res 6:1–34

    MathSciNet  MATH  Google Scholar 

  38. Xu WH, Yuan KH, Li WT (2022) Dynamic updating approximations of local generalized multigranulation neighborhood rough set. Appl Intell 52:9148–9173

    Google Scholar 

  39. Xu ZB, Liang JY, Dang CY, Chin KS (2002) Inclusion degree: a perspective on measures for rough set data analysis. Inform Sci 141:227–236

    MathSciNet  MATH  Google Scholar 

  40. Yang X, Li MM, Fujita H, Liu D, Li TR (2022) Incremental rough reduction with stable attribute group. Inform Sci 589:283–299

    Google Scholar 

  41. Yang XB, Liang SC, Yu HL, Gao S, Qian YH (2019) Pseudo-label neighborhood rough set: Measures and attribute reductions. Int J Approx Reason 105(2019):112–129

  42. Yang XB, Qi YS, Song XN, Yang YY (2013) Test cost sensitive multigranulation rough set: Model and minimal cost selection. Inform Sci 250:184–199

  43. Yang XL, Chen HM, Li TR, Wan JH, Sang BB (2021) Neighborhood rough sets with distance metric learning for feature selection. Knowl-Based Syst 224:107076

    Google Scholar 

  44. Yao YY (2019) Three-way conflict analysis: Reformulations and extensions of the pawlak model. Knowl-Based Syst 180:26–37

    Google Scholar 

  45. Yao YY, She YH (2016) Rough set models in multigranulation spaces. Inform Sci 327:40–56

    MathSciNet  MATH  Google Scholar 

  46. Yao YY, Zhao Y, Wang J (2008) On reduct construction algorithms. Trans Comput Sci 2:100–117

    MATH  Google Scholar 

  47. Zadeh LA (1997) Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst 90(2):111–127

  48. Zhang D, Zhu P (2022) Variable radius neighborhood rough sets and attribute reduction. Int J Approx Reason 150:98–121

    MathSciNet  MATH  Google Scholar 

  49. Zhu P (2011) An axiomatic approach to the roughness measure of rough sets. Fund Inform 109(4):463–480

    MathSciNet  MATH  Google Scholar 

  50. Zhu P, Wen QY (2012) Information-theoretic measures associated with rough set approximations. Inform Sci 212:33–43

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers and Editor for their insightful comments and suggestions which greatly improve the quality of this paper. This work was supported by the National Natural Science Foundation of China under Grant 62172048.

Author information

Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Jiayue Chen & Ping Zhu

  2. Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing, China

    Ping Zhu

Authors
  1. Jiayue Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ping Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ping Zhu.

Ethics declarations

Conflicts of interests

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, J., Zhu, P. A multigranulation rough set model based on variable precision neighborhood and its applications. Appl Intell 53, 24822–24846 (2023). https://doi.org/10.1007/s10489-023-04826-8

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-023-04826-8

Keywords

Search

Navigation