Skip to main content
SpringerLink
Log in

Three-way decisions in fuzzy incomplete information systems

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

Abstract

The intuitionistic fuzzy set is introduced to fuzzy incomplete information systems, the membership and non-membership degrees that an object belongs to a concept are constructed based on the similarity relation. By combining the fuzzy rough set and intuitionistic fuzzy set, we make three-way decisions. Various situations in fuzzy incomplete information systems are discussed.

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

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. Azam N, Yao JT (2012) Multiple criteria decision analysis withgame-theoretic rough sets. In: Li T, Nguyen HS, Wang G,Grzymala-Busse JW, Janicki R, Hassanien AE, Yu H (eds) RSKT 2012.LNCS(LNAI), vol. 7414. Springer, Heidelberg, pp 399–408

    Google Scholar 

  3. Bodjanova S (1997) Approximation of fuzzy concepts in decision making. Fuzzy Set Syst 8:23–29

    MathSciNet  MATH  Google Scholar 

  4. Cornelis C, Cock MD, Kerre EE (2003) Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert Syst 20:260–270

    Google Scholar 

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

    MATH  Google Scholar 

  6. Fan JC, Li Y, Tang LY, Wu GK (2018) RoughPSO: rough set-based particle swarm optimisation. Int J Bio-Inspired Comput 12(4):245–253

    Google Scholar 

  7. Grzymala-Busse JW, Yao YY (2011) Probabilistic rule induction with the LERS data mining system. Int J Intell Syst 26:518–539

    Google Scholar 

  8. He XL, Wei L, She YH (2018) L-fuzzy concept analysis for three-way decisions: basic definitions and fuzzy inference mechanisms. Int J Mach Learn Cybern 9(11):1857–1867

    Google Scholar 

  9. Herbert JP, Yao JT (2011) Game-theoretic rough sets. Fund Inf 108:267–286

    MathSciNet  MATH  Google Scholar 

  10. Hu MJ, Yao YY (2019) Structured approximations as a basis for three-way decisions in rough set theory. Int J Approx Reason 165:92–109

    Google Scholar 

  11. Jena SP, Ghosh SK (2002) Intuitionistic fuzzy rough sets. Notes Intuit Fuzzy Sets 8:1–18

    MathSciNet  MATH  Google Scholar 

  12. Jia F, Liu PD (2019) A novel three-way decision model under multiple-criteria environment. Inf Sci 471:29–51

    MathSciNet  Google Scholar 

  13. Jia XY, Li WW, Shang L (2019) A multiphase cost-sensitive learning method based on the multiclass three-way decision-theoretic rough set model. Inf Sci 485:248–262

    Google Scholar 

  14. Jia XY, Zhang K, Shang L (2012) Three-way decisions solution tofilter spam email: an empirical study. In: Yao JT, Yang Y, Slowinski R, Greco S, Li H, Mitra S, Polkowski L (eds) RSCTC 2012.LNCS(LNAI), vol 7413. Springer, Heidelberg, pp 287–296

    Google Scholar 

  15. Jiang C, Yao Y (2018) Effectiveness measures in movement-based three-way decisions. Knowl Based Syst 160:136–143

    Google Scholar 

  16. Kryszkiewicz M (1998) Rough set approach to incomplete information systems. Inf Sci 112(1):39–49

    MathSciNet  MATH  Google Scholar 

  17. Kryszkiewicz M (1999) Rules in incomplete information systems. Inf Sci 113(3):271–292

    MathSciNet  MATH  Google Scholar 

  18. Leung Y, Li D (2003) Maximal consistent block technique for rule acqusitioin in incomplete information systems. Inf Sci 153:85–106

    MATH  Google Scholar 

  19. Leung Y, Wu WZ, Zhang WX (2006) Knowledge acquisition in incomplete information systems: a rough set approach. Eur J Oper Res 168(1):164–180

    MathSciNet  MATH  Google Scholar 

  20. Li HX, Zhou XZ (2011) Risk decision making based on decision-theoretic rough set: a three-way view decision model. Int J Comput Intell Syst 4:1–11

    Google Scholar 

  21. Li JY, Wang X, Wu WZ, Xu YH (2017) Attribute reduction in inconsistent formal decision contexts based on congruence relations. Int J Mach Learn Cybern 8(1):81–94

    Google Scholar 

  22. Li W, Miao DQ, Wang WL, Zhang N (2010) Hierarchical rough decision theoretic framework for text classification. In: Proceedings of the 9th ieee international conference on cognitive informatics, pp 484–489

  23. Liang DC, Xu ZS, Liu D, Wu Y (2018) Method for three-way decisions using ideal TOPSIS solutions at Pythagorean fuzzy information. Inf Sci 435:282–295

    MathSciNet  Google Scholar 

  24. Liu D, Li TR, Li HX (2012) A multiple-category classification approach with decision-theoretic rough sets. Fund Inf 115:173–188

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  26. Liu D, Liang DC (2017) Three-way decisions in ordered decision system. Knowl Based Syst 137:182–195

    Google Scholar 

  27. Luo C, Li TR, Huang Y, Fujita H (2019) Updating three-way decisions in incomplete multi-scale information systems. Inf Sci 476:274–289

    Google Scholar 

  28. Ma XA, Yao YY (2018) Three-way decision perspectives on class-specific attribute reducts. Inf Sci 450:227–245

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  30. Qian J, Liu CH, Yue XD (2019) Multigranulation sequential three-way decisions based on multiple thresholds. Int J Approx Reason 105:396–416

    MathSciNet  MATH  Google Scholar 

  31. Ren RS, Wei L, Yao YY (2018) An analysis of three types of partially-known formal concepts. Int J Mach Learn Cybern 9(11):1767–1783

    Google Scholar 

  32. Radziknowska AM (2006) Rough approximation operations based on IFsets. In: Rutkkowski L, Tadeusiewicz R, Zadeh LA, Aurada JM (eds)ICAISC 2006, LNCS(LNAI), vol 4029. Springer,Heidelberg, pp 528–537

  33. Wang R, Wang XZ, Kwong S, Xu C (2017) Incorporating diversity and informativeness in multiple-instance active learning. IEEE Trans Fuzzy Syst 25(6):1460–1475

    Google Scholar 

  34. Wang XZ, Wang R, Xu C (2018) Discovering the relationship between generalization and uncertainty by incorporating complexity of classification. IEEE Trans Cybern 48(2):703–715

    MathSciNet  Google Scholar 

  35. Wang XZ, Xing HJ, Li Y, Hua Q, Dong CR, Pedrycz W (2015) A study on relationship between generalization abilities and fuzziness of base classifiers in ensemble learning. IEEE Trans Fuzzy Syst 23(5):1638–1654

    Google Scholar 

  36. Wang XZ, Zhang T, Wang R (2019) Noniterative deep learning: incorporating restricted boltzmann machine into multilayer random weight neural networks. IEEE Trans Syst Man Cybern Syst 49(7):1299–1308

    Google Scholar 

  37. Wong SKM, Ziarko W (1985) A probabilistic model of approximate classification and decision rules with uncertainty in inductive learning, Technical report CS-85-23. University of Regina, Department of Computer Science

    Google Scholar 

  38. Wong SKM, Ziarko W (1987) Comparison of the probabilistic approximate classification and the fuzzy set model. Fuzzy Set Syst 21:357–362

    MathSciNet  MATH  Google Scholar 

  39. Wu WZ, Mi JS, Zhang WX (2003) A generalized fuzzy rough sets. Inf Sci 151:263–282

    MathSciNet  MATH  Google Scholar 

  40. Wu WZ, Zhang WX, Li HZ (2003) Knowledge acquisition in incomplete fuzzy information systems via rough set approach. Expert Syst 20(5):280–286

    Google Scholar 

  41. Wu WZ, Zhang WX (2004) Constructive and axiomatic approaches of fuzzy approximation operators. Inf Sci 159(3–4):233–254

    MathSciNet  MATH  Google Scholar 

  42. Yang X, Li TR, Fujita H, Liu D (2019) A sequential three-way approach to multi-class decision. Int J Approx Reason 104:108–125

    MathSciNet  MATH  Google Scholar 

  43. Yang XP, Yao JT (2012) Modelling multi-agent three-way decisions with decision-theoretic rough sets. Fund Inf 115:157–171

    MathSciNet  MATH  Google Scholar 

  44. Yang XP, Lu ZJ, Li TJ (2013) Decision-theoretic rough sets in incomplete information system. Fund Inf 126:353–375

    MathSciNet  Google Scholar 

  45. Yang XP, Tan AH (2017) Three-way decisions based on intuitionisticfuzzy sets. In: Polkowski L, Yao Y, Artiemjew P, Ciucci D, Liu D, Slezak D, Zielosko B (eds) IJCRS 2017, LNCS(LNAI), vol. 10314, pp.290–299. Springer, Heideberg

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

    Google Scholar 

  47. Yao YY (2007) Decision-theoretic rough set models. In: Yao J, Lingras P, Wu WZ, Szczuka M, Cercone NJ, Slezak D (eds) RSKT 2007, LNCS(LNAI), vol 4481. Springer, Heidelberg, pp 1–12

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

    Google Scholar 

  49. Yao YY (2008) Probabilistic rough set approximations. Int J Approx Reason 49:255–271

    MATH  Google Scholar 

  50. Yao YY (2009) Three-way decision: an interpretation of rules inrough set theory. In: Wen P, Li Y, Polkowski L, Yao Y, Tsumoto H,Wang G (eds) RSKT 2009, LNCS (LNAI), vol 5589. Springer, Heidelberg, pp 642–649

    Google Scholar 

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

    MathSciNet  Google Scholar 

  52. Yao YY (2011) The superiority of three-way decisions in probabilistic rough set models. Inf Sci 181:1080–1096

    MathSciNet  MATH  Google Scholar 

  53. Yao YY (2012) An outline of a theory of three-way decisions. In: Yao JT, Yang Y, Slowinski R, Greco S, Li H, Mitra S, Polkowski L (eds) RSCTC 2012, LNCS (LNAI), vol 7413. Springer,Heidelberg, pp 287–296

  54. Yao YY (2018) Three-way decision and granular computing. Int J Approx Reason 103:107–123

    MATH  Google Scholar 

  55. Yu H, Chu SS, Yang DC (2012) Autonomous knowledge-oriented clustering using decision-theoretic rough set theory. Fund Inf 115:141–156

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  57. Zhang QH, Lv QX, Chen YH, Wang GY (2018) A dynamic three-way decision model based on the updating of attribute values. Knowl Based Syst 142:71–84

    Google Scholar 

  58. Zhang WX, Leung Y, Wu WZ (2003) Information system and knowledge discovery. Science Press, Beijing

    Google Scholar 

  59. Zhou JH, Zhang Y, Zhu HY (2017) Three-way decisions model based on tolerance rough fuzzy set. Int J Mach Learn Cybern 8(1):35–43

    Google Scholar 

  60. Zhou L, Wu WZ (2008) On generalized intuitionistic fuzzy rough approximation operators. Inf Sci 178:2448–2465

    MathSciNet  MATH  Google Scholar 

  61. Ziarko W (1993) Variable precision rough set model. J Comput Syst Sci 46(93):39–50

    MathSciNet  MATH  Google Scholar 

  62. Ziarko W (2008) Probabilistic approach to rough sets. Int J Approx Reason 49:272–284

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by grants from National Natural Science Foundation of China (Nos. 61773349 and 61602415).

Author information

Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Xiaoping Yang, Tongjun Li & Anhui Tan

  2. Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, 316022, Zhejiang, People’s Republic of China

    Xiaoping Yang, Tongjun Li & Anhui Tan

Authors
  1. Xiaoping Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tongjun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anhui Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoping Yang.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, X., Li, T. & Tan, A. Three-way decisions in fuzzy incomplete information systems. Int. J. Mach. Learn. & Cyber. 11, 667–674 (2020). https://doi.org/10.1007/s13042-019-01025-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-019-01025-1

Keywords

Search

Navigation