Skip to main content
SpringerLink
Log in

Three-way decisions model based on tolerance rough fuzzy set

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Based on Bayesian decision theory, three-way decisions model (TWDM) proposed by Yao gives new semantic interpretations of positive region, negative region and boundary region. Some extensions of TWDM have been proposed by different authors and have been successfully applied to many fields, such as soft computing, data mining and decision making. However existing three-way decisions models are almost developed in certainty environment, which limits their applications in uncertainty environment. In order to deal with this problem, based on tolerance rough fuzzy set, a TWDM is proposed in this paper. The main contributions of this paper include two aspects: (1) the tolerance rough fuzzy set which is extended from rough fuzzy set is introduced, and some basic properties of the tolerance rough fuzzy set are investigated. (2) The TWDM with respect to the tolerance rough fuzzy set is proposed. In addition, an example is given to illustrate the computation processes of the TWDM.

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

Similar content being viewed by others

References

  1. Pawlak Z (1982) Rough sets. Int J Inf Comput Sci 11:341–356

    Article  MathSciNet  MATH  Google Scholar 

  2. Zhou W, Zhang SL (2015) The decision delay in finite-length MMSE–DFE systems. Wirel Pers Commun 83(1):175–189

    Article  Google Scholar 

  3. He S, Chen HH, Zhu ZX et al (2015) Robust twin boosting for feature selection from high-dimensional OMICS data with label noise. Inf Sci 291:1–18

    Article  Google Scholar 

  4. Pan F, Song GG, Gan XB et al (2014) Consistent feature selection and its application to face recognition. J Intell Inf Syst 43(2):307–321

    Article  Google Scholar 

  5. Zhu ZX, Jia S, Ji Z (2010) Towards a memetic feature selection paradigm. IEEE Comput Intell Mag 5(2):41–53

    Article  Google Scholar 

  6. Xie JY, Hone K, Xie WX et al (2013) Extending twin support vector machine classifier for multi-category classification problems. Intell Data Anal 17(4):649–664

    Google Scholar 

  7. Yang R, Ren OY (2014) Classification based on Choquet integral. J Intell Fuzzy Syst 27(4):1693–1702

    MathSciNet  MATH  Google Scholar 

  8. Yang R, Wang ZY (2015) Cross-oriented choquet integrals and their applications on data classification. J Intell Fuzzy Syst 28(1):205–216

    MathSciNet  MATH  Google Scholar 

  9. He YL, Wang XZ, Huang ZX (2016) Recent advances in multiple criteria decision making techniques. Int J Mach Learn Cybern. doi:10.1007/s13042-015-0490-y

  10. Ziarko W (1993) Variable precision rough set model. J Comput Syst Sci 46(93):39–59

    Article  MathSciNet  MATH  Google Scholar 

  11. Yao YY (2003) Probabilistic approaches to rough sets. Expert Syst 20(5):287–297

    Article  Google Scholar 

  12. Yao YY, Wong SKM (1992) A decision theoretic framework for approximating concepts. Int J Man Mach Stud 37(6):793–809

    Article  Google Scholar 

  13. Li WT, Xu WH (2015) Double-quantitative decision-theoretic rough set. Inf Sci 316:54–67

    Article  Google Scholar 

  14. Dou HL, Yang XB, Song XN et al (2016) Decision-theoretic rough set: a multicost strategy. Knowl Based Syst 91:71–83

    Article  Google Scholar 

  15. Yao YY, Lin TY (1996) Generalization of rough sets using modal logics. Intell Autom Soft Comput Int J 2(2):103–120

    Article  Google Scholar 

  16. Skowron A (2000) Tolerance approximation spaces. Fundam Inf 64(2–3):245–253

    MathSciNet  MATH  Google Scholar 

  17. Greco S, Matarazzo B, Slowinski R (1999) Rough approximation of a preference relation by dominance relations. Eur J Oper Res 117(98):63–83

    Article  MATH  Google Scholar 

  18. Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17(2):191–208

    Article  MATH  Google Scholar 

  19. Kuncheva LI (1992) Fuzzy rough sets: application to feature selection. Fuzzy Sets Syst 51(2):147–153

    Article  MathSciNet  Google Scholar 

  20. Nanda S (1992) Fuzzy rough sets. Fuzzy Sets Syst 45(2):157–160

    Article  MathSciNet  MATH  Google Scholar 

  21. Yao YY (1997) Combination of rough and fuzzy sets based on-level sets. In: Lin TY, Cercone N (eds) Rough sets and data mining: analysis for imprecise data. Kluwer Academic Publishers, Boston, pp 301–321

    Chapter  Google Scholar 

  22. Chen Y (2015) An adjustable multigranulation fuzzy rough set. Int J Mach Learn Cybern 7(2):1–8

    Google Scholar 

  23. Zhang C, Li DY, Liang JY (2016) Hesitant fuzzy linguistic rough set over two universes model and its applications. Int J Mach Learn Cybern. doi:10.1007/s13042-016-0541-z

  24. Zhao SY, Chen H, Li CP et al (2014) RFRR: robust fuzzy rough reduction. IEEE Trans Fuzzy Syst 21(5):825–841

    Article  Google Scholar 

  25. Zhao SY, Tsang ECC, Chen DG et al (2009) Building a rule-based classifier—a fuzzy-rough set approach. IEEE Trans Knowl Data Eng 22(5):624–638

    Article  Google Scholar 

  26. Zhao SY, Chen H, Li CP et al (2015) A novel approach to building a robust fuzzy rough classifier. IEEE Trans Fuzzy Syst 23(4):769–786

    Article  MathSciNet  Google Scholar 

  27. Wang XZ, Xing HJ, Li Y et al (2015) A study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning. IEEE Trans Fuzzy Syst 23(5):1638–1654

    Article  Google Scholar 

  28. Wang XZ, Ashfaq RAR, Fu AM (2015) Fuzziness based sample categorization for classifier performance improvement. J Intell Fuzzy Syst 29(3):1–12

    MathSciNet  Google Scholar 

  29. Wang XZ (2015) Learning from big data with uncertainty—editorial. J Intell Fuzzy Syst 28(5):2329–2330

    Article  MathSciNet  Google Scholar 

  30. Ashfaq RAR, Wang XZ, Huang JZX et al (2016) Fuzziness based semi-supervised learning approach for intrusion detection system. Inf Sci. doi:10.1016/j.ins.2016.04.019

  31. He YL, Wang XZ, Huang JZX (2016) Fuzzy nonlinear regression analysis using a random weight network. Inf Sci 364–365:222–240

    Article  Google Scholar 

  32. He YL, Liu JNK, Hu YX et al (2015) OWA operator based link prediction ensemble for social network. Expert Syst Appl 42(1):21–50

    Article  Google Scholar 

  33. Gong ZT, Zhang XX (2016) The further investigation of variable precision intuitionistic fuzzy rough set model. Int J Mach Learn Cybern. doi:10.1007/s13042-016-0528-9

  34. Yao YY (2010) Three-way decisions with probabilistic rough sets. Inf Sci 180(3):341–353

    Article  MathSciNet  Google Scholar 

  35. Fujita H, Li TR, Yao YY (2016) Advances in three-way decisions and granular computing. Knowl Based Syst 91:1–3

    Article  Google Scholar 

  36. Liu D, Liang DC, Wang CC (2016) A novel three-way decision model based on incomplete information system. Knowl Based Syst 91:32–45

    Article  Google Scholar 

  37. Liang DC, Liu D, Kobina A (2016) Three-way group decisions with decision-theoretic rough sets. Inf Sci 345:46–64

    Article  Google Scholar 

  38. Zhao XR, Hu BQ (2016) Fuzzy probabilistic rough sets and their corresponding three-way decisions. Knowl Based Syst 91:126–142

    Article  Google Scholar 

  39. Chen YM, Zeng ZQ, Zhu QX et al (2016) Three-way decision reduction in neighborhood systems. Appl Soft Comput 38:942–954

    Article  Google Scholar 

  40. Peters JF, Ramanna S (2016) Proximal three-way decisions: theory and applications in social networks. Knowl Based Syst 91:4–15

    Article  Google Scholar 

  41. Zhang HR, Min F, Shi B (2016) Regression-based three-way recommendation. Inf Sci. doi:10.1016/j.ins.2016.03.019

  42. Li HX, Zhang LB, Huang B et al (2016) Sequential three-way decision and granulation for cost-sensitive face recognition. Knowl Based Syst 91:241–251

    Article  Google Scholar 

  43. Li WW, Huang ZQ, Li Q (2016) Three-way decisions based software defect prediction. Knowl Based Syst 91:263–274

    Article  Google Scholar 

  44. Yang HL, Guo ZL (2015) Multigranulation decision-theoretic rough sets in incomplete information systems. Int J Mach Learn Cybern 6(6):1005–1018

    Article  Google Scholar 

  45. Li JH, Huang CC, Qi JJ (2016) Three-way cognitive concept learning via multi-granularity. Inf Sci. doi:10.1016/j.ins.2016.04.051

  46. Liang DC, Liu D (2015) Deriving three-way decisions from intuitionistic fuzzy decision-theoretic rough sets. Inf Sci 300:28–48

    Article  MathSciNet  Google Scholar 

  47. Hu BQ (2014) Three-way decisions space and three-way decisions. Inf Sci 281:21–52

    Article  MathSciNet  Google Scholar 

  48. Hu BQ (2016) Three-way decision spaces based on partially ordered sets and three-way decisions based on hesitant fuzzy sets. Knowl Based Syst 91:16–31

    Article  Google Scholar 

  49. Yao YY (2016) Interval sets and three-way concept analysis in incomplete contexts. Int J Mach Learn Cybern. doi:10.1007/s13042-016-0568-1

  50. Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This research is supported by Basic Research Project of Knowledge Innovation Program in Shenzhen (JCYJ20150324140036825), by National Natural Science Foundations of China (71371063), by Key Scientific Research Foundation of Education Department of Hebei Province (ZD20131028).

Author information

Authors and Affiliations

  1. Key Lab. of Machine Learning and Computational Intelligence, College of Mathematics and Information Science, Hebei University, Baoding, 071002, Hebei, China

    Junhai Zhai

  2. College of Computer Science and Technology, Hebei University, Baoding, 071002, Hebei, China

    Yao Zhang

  3. College of Computer Science and Software, Shenzhen University, Shenzhen, 518060, China

    Hongyu Zhu

Authors
  1. Junhai Zhai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongyu Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Junhai Zhai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhai, J., Zhang, Y. & Zhu, H. Three-way decisions model based on tolerance rough fuzzy set. Int. J. Mach. Learn. & Cyber. 8, 35–43 (2017). https://doi.org/10.1007/s13042-016-0591-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-016-0591-2

Keywords

Search

Navigation