Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Topological approach to multigranulation rough sets

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

Abstract

For further studying the theory of multigranulation rough sets, we attempt to investigate a new theory on multigranulation rough sets from the topological view in this paper. We firstly explore multigranulation topological rough space and its topological properties by giving some new definitions and theorems. Then, topological granularity and topological entropy are proposed to characterize the uncertainty of a multigranulation topological rough space. Finally, based on the invariance of interior and closure operators of a target concept, a granulation selection algorithm is introduced to deal with the granularity selection issue in the multigranulation rough data analysis.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Abo-Tabl EA (2012) Rough sets and topological spaces based on similarity. J Mach Learn Cybern. doi:10.1007/s13042-012-0107-7

  2. Bonikowski Z, Brynirski E, Wybraniec U (1998) Extensions and intentions in the rough set theory. Inf Sci 107:149–167

    Article  MATH  Google Scholar 

  3. Chen JK, Li JJ, Lin YJ (2012) On the structure of definable sets in covering approximation spaces. J Mach Learn Cybern. doi:10.1007/s13042-012-0086-8

  4. Chen DG, Wang CZ, Hu QH (2007) A new approach to attribute reduction of consistent and inconsistent covering decision systems with covering rough sets. Inf Sci 177:3500–3518

    Article  MATH  Google Scholar 

  5. Chen DG, Zhang WX (2001) Rough sets and topology space. J Xi’an Jiaotong University 35(12):1313–1315 (in Chinese)

    MATH  Google Scholar 

  6. Ciobanu G, Rusa D(2006) A topological approach of the web classification. Lect Notes Comput Sci 4281:80–92

    Article  Google Scholar 

  7. Fang J (2007) L-fuzzy Alexandrov topologies and specialization orders. Fuzzy Sets Syst 158:2359–2374

    Article  MATH  Google Scholar 

  8. Jarvinen J, Kortelainen J (2007) A unifying study between model-like operators, topologies, and fuzzy sets. Fuzzy Sets Syst 158:1217–1225

    Article  MathSciNet  Google Scholar 

  9. Kelley J (1995) General topology. Van Nostrand Company

  10. Kondo M (2006) On the structure of generalized rough sets. Inf Sci 176:589–600

    Article  MATH  Google Scholar 

  11. Kortelainen J (1994) On relationship between modified sets, topology spaces and rough sets. Fuzzy Sets Syst 61:91–95

    Article  MATH  MathSciNet  Google Scholar 

  12. Kang XP, Li DY (2012) Dependency space, closure system and rough set theory. International J Mach Learn Cybern. doi:10.1007/s13042-012-0106-8

  13. Khan Md.A, Banerjee M (2008) Formal reasoning with rough sets in multiple-source approximation systems. Int J Approx Reason 49:466–477

    Article  MATH  MathSciNet  Google Scholar 

  14. Lai H, Zhang D (2006) Fuzzy preorder and fuzzy topology. Fuzzy Sets Syst 157:1865–1885

    Article  MATH  MathSciNet  Google Scholar 

  15. Lashin EF, Kozae AM, Abo-Khadra AA, Medhat T (2005) Rough set theory for topology spaces. Int J Approx Reason 40:35–43

    Article  MATH  MathSciNet  Google Scholar 

  16. Li JH, Mei CL, Lv YJ (2012) Knowledge reduction in real decision formal contexts. Inf Sci 189:191–207

    Article  MATH  MathSciNet  Google Scholar 

  17. Pei D, Xu Z (2007) Transformation of rough set models. Knowl Based Syst 20(8):745–751

    Article  Google Scholar 

  18. Rasiowa H (1974) An Algebraic Approach to Non-classical Logic. North-Holland, Amsterdam

    Google Scholar 

  19. Lee TT (1987) An information-theoretic analysis of relational database, part I: data dependencies and information metric. IEEE Trans Soft Engin 13:1049–1061

    Article  Google Scholar 

  20. Liang JY, Wang F, Dang CY, Qian YH (2012) An efficient rough feature selsction algorithm with a multi-granulation view. Int J Appro Reason 53(7):1080–1093

    Article  MathSciNet  Google Scholar 

  21. Lin TY (1992) Topological and fuzzy rough sets In: Slowinski R (ed) Decision Support by Experience-Application of the Rough Sets Theory. Kluwer, Norwell,pp 287–304

  22. Lin TY, Liu Q, Yao YY (1994) Logic systems for approximate reasoning: Via rough sets and topology in Methodologies for Intelligent Systems.Springer-Verlag, Berlin

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  24. Liu CH, Wang MZ (2011) Covering fuzzy rough set based on multi-granulations. Int Conf Uncertainty Reason Knowl Engineering :146–149

  25. Liu CH, Miao DQ (2011) Covering rough set model based on multigranulations, RSFDGRc2011 87-90

  26. Polkowski L (2001) On fractals defined in information systems via rough set theory. In: Proceedings of the RSTGC-2001. Bull Int Rough Set Society, vol 5, pp 163–166

  27. Polkowski L, Semeniuk-Polkowska M (2004) Some remarks on sets of communicating sequential processes in topological rough set framework. Fundam Inform 60:291–305

    MATH  MathSciNet  Google Scholar 

  28. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 5:341–356

    Article  MathSciNet  Google Scholar 

  29. Pawlak Z (1991) Rough sets: theoretical aspects of reasoning about data. Kluwer, Dordrecht

    Book  MATH  Google Scholar 

  30. Pei D, Xu Z (2004) Rough set models on two universes. Int J Gen Syst 332(5):569–581

    Article  MathSciNet  Google Scholar 

  31. Pei Z, Pei. DW, Zheng L (2011) Topology vs generalized rough sets. Int J Approx Reason 52:231–239

    Article  MATH  MathSciNet  Google Scholar 

  32. Pomykala JA (1987) Approximation operations in approximation space. Bull Polish Academic Sci 35(9–10):653–662

    MATH  MathSciNet  Google Scholar 

  33. Qian YH, Liang JY (2006) Rough set model based on multigranulations. In: Proceedings of 5th IEEE Conference on Cognitive Informatics. China I 297-304

  34. Qian YH, Liang JY, Yao YY, Dang CY (2010) MGRS: A multi-granulation rough set. Inf Sci 180:949–970

    Article  MATH  MathSciNet  Google Scholar 

  35. Qian YH, Liang JY (2011) Granulation mechanism and data modeling for complex data. Phd thesis, Shanxi University

  36. Qina K, Pei Z (2005) On the topological properties of fuzzy rough sets. Fuzzy Sets Syst 151(3):601–613

    Article  Google Scholar 

  37. Qin K, Pei Z (2005) On the topological properties of fuzzy rough sets. Fuzzy Sets Syst 151:601–613

    Article  MATH  MathSciNet  Google Scholar 

  38. She YH, He XL (2012) On the structure of the multigranulation rough set model. Knowl Based Syst 36:81–92

    Article  Google Scholar 

  39. Slowinski R, Vanderpooten D (2000) A generalized definition of rough approximations based on similarity. IEEE Trans Knowl Data Eng 12:331–336

    Article  Google Scholar 

  40. Srivastava AK, Tiwari SP (2003) On relationships among fuzzy approximation operators, fuzzy topology, and fuzzy automata. Fuzzy Sets Syst 138:197–204

    Article  MATH  MathSciNet  Google Scholar 

  41. Skowron A (1988) On the topology in information systems. Bull Polish Academy Sciences-Mathematics 36:477–480

    MATH  MathSciNet  Google Scholar 

  42. Xu WH, Wang QR, Zhang XT(2011) Multi-granulation fuzzy rough sets in a fuzzy tolerance approximation space. In J Fuzzy Syst 13(4):246–259

    MathSciNet  Google Scholar 

  43. Wang CZ, Chen DG , Hu QH (2012) On rough approximations of groups. Int J Mach Learn Cybern. doi:10.1007/s13042-012-0108-6

  44. Yang XB, Song XN, Dou HL(2011) Multi-granulation rough set: from crisp to fuzzy case. Annals Fuzzy Math Inf 1(1):55–70

    MathSciNet  Google Scholar 

  45. Wiweger A (1988) On topological rough sets. Bull Polish Acad Sci Math 37:51–62

    Google Scholar 

  46. Wu QE, Wang T, Huang YX, Li JS (2008) Topology theory on rough sets. IEEE Trans Syst Man Cybernetics part Cybernet 1(38):68–77

    Article  Google Scholar 

  47. Yao YY (1996) Two views of the theory of rough sets in finite universes. Int J Approx Reason 15:291–317

    Article  MATH  Google Scholar 

  48. Yao YY (1998) Constructive and algebraic methods of the theory of rough sets. Inf Sci 109:21–47

    Article  MATH  Google Scholar 

  49. Yang LY, Xu LS (2011) Topological properties of generalized approximation spaces. Inf Sci 182(17):3570–3580

    Article  Google Scholar 

  50. Zakowski W (1983) Approximations in the space \((U, \Uppi)\). Demons Mathematica 16:761–769

    MATH  MathSciNet  Google Scholar 

  51. Zhu W (2007) Topological approaches to covering rough sets. Inf Sci 177(6):1499–1508

    Article  MATH  Google Scholar 

  52. Zhu W, Wang FY (2007) On three types of covering rough sets. IEEE Trans Knowl Data Eng 19(8):1131–1144

    Article  Google Scholar 

  53. Zhu W, Wang FY (2003) Reduction and axiomization of covering generalized rough sets. Inf Sci 152(1):217–230

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers and the editor for their constructive and valuable comments. This work is supported by grants from National Natural Science Foundation of China under Grant (No. 71031006), National Key Basic Research and Development Program of China (973) (No. 2013CB329404), Innovative Talents of Higher Learning Institutions of Shanxi, China (No. 20120301), and Education Committee of Fujian Province under Grant (Nos. JK2011031).

Author information

Authors and Affiliations

  1. Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, 030006, Shanxi, People’s Republic of China

    Guoping Lin, Jiye Liang & Yuhua Qian

  2. Department of Mathematics and Information Science, Zhangzhou Normal University, Zhangzhou, 363000, People’s Republic of China

    Guoping Lin

Authors
  1. Guoping Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiye Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuhua Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiye Liang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lin, G., Liang, J. & Qian, Y. Topological approach to multigranulation rough sets. Int. J. Mach. Learn. & Cyber. 5, 233–243 (2014). https://doi.org/10.1007/s13042-013-0160-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-013-0160-x

Keywords

Search

Navigation