Skip to main content
SpringerLink
Log in

Fuzzy rough set models over two universes

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

Abstract

The extension of rough set model is an important research direction in rough set theory. The aim of this paper is to present new extensions of the rough set model over two different universes which are rough fuzzy set model in a generalized approximation space, rough set model in a fuzzy approximation space and rough fuzzy set model in a fuzzy approximation space based over two different universes. Moreover, the properties of the approximation operators in these models are investigated. Furthermore, by employing cut set of fuzzy set and fuzzy relation, classical representations of fuzzy rough approximation operators are studied. Finally, the measures of fuzzy rough set models are presented, and the relationships among the fuzzy rough models and rough set model over two universes are investigated.

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. Ananthanarayana VS, Narasimha MM, Subramanian DK (2003) Tree structure for efficient data mining using rough sets. Pattern Recognit Lett 24:851–862

    Article  MATH  Google Scholar 

  2. Cheng W, Mo ZW, Wang J (2007) Notes on the lower and upper approximations in a fuzzy group and rough ideals in semigroups. Inf Sci 177:5134–5140

    Article  MathSciNet  MATH  Google Scholar 

  3. Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17:191C209

    Article  Google Scholar 

  4. Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38:325–339

    Article  MathSciNet  MATH  Google Scholar 

  5. Dntsch I, Gediga G (1998) Uncertainty measures of rough set prediction. Artif Intell 106:109–137

    Article  Google Scholar 

  6. Gong ZT, Sun BZ, Chen DG (2008) Rough set theory for the interval-valued fuzzy information systems. Inf Sci 178:1968–1985

    Article  MathSciNet  MATH  Google Scholar 

  7. He Q, Wu CX (2011) Membership evaluation and feature selection for fuzzy support vector machine based on fuzzy rough sets. Soft Comput 15(6):1105–1114

    Article  MathSciNet  Google Scholar 

  8. Järiner J (2001) Approximations and rough sets based on tolerances. Inf Sci 177:182–189

    Google Scholar 

  9. Jensen R, Shen Q (2007) Fuzzy-rough sets assisted attribute selection. IEEE Trans Fuzzy Syst 15:73–89

    Article  Google Scholar 

  10. Li TJ, Zhang WX (2008) Rough fuzzy approximations on two universes of discourse. Inf Sci 178:892–906

    Article  MATH  Google Scholar 

  11. Liu GL (2010) Rough set theory based on two universal sets and its applications. Knowl-Based Syst 23:110–115

    Article  Google Scholar 

  12. Mi JS, Zhang WX (2004) An axiomatics characterization of a fuzzy generalization of rough sets. Inf Sci 160:235–249

    Article  MathSciNet  MATH  Google Scholar 

  13. OuYang Y, Wang ZD, Zhang HP (2010) On fuzzy rough sets based on tolerance relations. Inf Sci 180:532–542

    Article  MathSciNet  MATH  Google Scholar 

  14. Pomykala JA (2002) Rough sets and current trends in computing: about tolerance and similarity relations in information systems, vol 2475. Springer, Berlin/Heidelberg, pp 175–182

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

    Article  MathSciNet  MATH  Google Scholar 

  16. Pawlak Z (1991) Rough set: theoretical aspects of reasoning about data. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  17. Pawlak Z (1994) Rough sets approach to multi-attribute decision analysis. Eur J Oper Res 72:443–459

    Article  MATH  Google Scholar 

  18. Pawlak Z (2002) Rough sets, decision algorithms and Bayes’s theorem. Eur J Oper Res 136:181–189

    Article  MathSciNet  MATH  Google Scholar 

  19. Pawlak Z (2005) Some remarks on conflict analysis. Eur J Oper Res 166:649–654

    Article  MATH  Google Scholar 

  20. Pawlak Z, Skowron A (2007) Rudiments of rough sets. Inf Sci 177:3–27

    Article  MathSciNet  MATH  Google Scholar 

  21. Pei DW, Xu ZB (2004) Rough set models on two universes. Int J Gen Syst 33:569–581

    Article  MathSciNet  MATH  Google Scholar 

  22. Shu L, He XZh (2007) Rough set model with double universe of discourse. In: IEEE international conference on information reuse and integration, pp 492-495

  23. Shen YH, Wang FX (2010) Variable precision rough set model over two universes and its properties. Soft Comput A Fusion Found Methodol Appl

  24. Sun BZ, Ma WM (2011) Fuzzy rough set model on two different universes and its application. Appl Math Model 35:1798–1809

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang XZ, Tsang E, Zhao SY, Chen DG, Yeung D (2007) Learning fuzzy rules from fuzzy examples based on rough set techniques. Inf Sci 177(20):4493–4514

    Article  MathSciNet  MATH  Google Scholar 

  26. Wang XZ, Zhai JH, Lu SX (2008) Induction of multiple fuzzy decision trees based on rough set technique. Inf Sci 178(16):3188–3202

    Article  MathSciNet  MATH  Google Scholar 

  27. Wu WZ, Mi JS, Zhang WX (2003) Generalized fuzzy rough sets. Inf Sci 15:263–282

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  Google Scholar 

  29. Wu WZ, Zhang WX, Xu ZB (2004) Characterizating rough fuzzy sets in constructive and axiomatic approaches. Chin J Comput 27:197–203

    MathSciNet  Google Scholar 

  30. Xu WH, Liu SH, Zhang WX (2010) Upper approximation reduction in ordered information system with fuzzy decision. Int J Comput Sci Knowl Eng 4:111–114

    MathSciNet  Google Scholar 

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

  32. Yan RX, Zheng JG, Liu JL, Zhai YM (2010) Research on the model of rough set over dual-universes. Knowl-Based Syst 23:817–822

    Article  Google Scholar 

  33. Yang XB, Song XN, Chen ZH, Yang JY (2011) On multigranulation rough sets in incomplete information system. Int J Mach Learn Cybern. doi:10.1007/s13042-011-0054-8

  34. Zhou L, Wu WZ (2011) Characterization of rough set approximation in Atanassov intuitionistic fuzzy set theory. Comput Math Appl, pp 1–15

  35. Zhang HY, Zhang WX, Wu WZ (2009) On characterization of the generalized interval-valued fuzzy rough sets on two universes of discourse. Int J Approx Reason, pp 1–15

  36. Zhao SX, Zhang ZR (2005) A generalized definition of rough approximation based on similarity in variable precision rough sets. In: The fourth international conference on machine learning and cybernetics, Guangzhou, pp 3153–3156

  37. Zhai JH (2011) Fuzzy decision tree based on fuzzy-rough technique. Soft Comput 15(6):1087–1096

    Article  Google Scholar 

  38. Zhu W, Wang SP (2011) Matroidal approaches to generalized rough sets based on relations. Int J Mach Learn Cybern 2(4):273–279

    Article  Google Scholar 

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

Download references

Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions. This work is supported by National Natural Science Foundation of China (No.61105041,71071124,11071284 and 11001227), National Natural Science Foundation of CQ CSTC (No. cstc2011jjA40037), Science and Technology Program of Board of Education of Chongqing (KJ120805) and Graduate Innovation Foundation of Chongqing University of Technology (No.YCX2011312).

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, 400054, People’s Republic of China

    Weihua Xu, Wenxin Sun & Yufeng Liu

  2. School of Science, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Wenxiu Zhang

Authors
  1. Weihua Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenxin Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yufeng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenxiu Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Weihua Xu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, W., Sun, W., Liu, Y. et al. Fuzzy rough set models over two universes. Int. J. Mach. Learn. & Cyber. 4, 631–645 (2013). https://doi.org/10.1007/s13042-012-0129-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-012-0129-1

Keywords

Search

Navigation