Skip to main content
SpringerLink
Log in

Topological approaches to generalized definitions of rough multiset approximations

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

Abstract

This paper proposes new definitions of lower and upper multiset approximations, which are basic concepts of the rough multiset theory. These definitions come naturally from the concepts of multiset topology and the concepts of ambiguity introduced in this paper. The new definitions are compared to the classical definitions and are shown to be more general. In the sense that they are the only ones which can be used for any type of indiscernibility or similarity multiset relation.

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

  2. Abo-Tabl EA Topological rough multisets. (submitted)

  3. Blizard WD (1989) Multiset theory. Notre Dame J Logic 30:346–368

    MathSciNet  Google Scholar 

  4. Chan CC (2004) Learning rules from very large databases using rough multisets, Transaction on Rough Sets, vol 1. LNCS 3100:59–77

    Google Scholar 

  5. Chang Y-C, Chu C-P (2010) Applying learning behavioral Petri nets to the analysis of learning behavior in web-based learning environments. Inform Sci 180:995–1009

    Article  MathSciNet  Google Scholar 

  6. Chen J, Li J, Lin Y (2013) on the structure of definable sets in covering approximation spaces. Int J Mach Learn Cybern 4:195–206

    Article  Google Scholar 

  7. Fan T, Pei D (2007) Topological description of rough set models. in: Proceedings of the IEEE international conference on fuzzy sets and knowledge discovery 2007, Haikou, China, August 24-27, vol 3, pp 229–232

  8. Girish KP, John SJ (2009) Relations and functions in multiset context. Inform Sci 179:758–768

    Article  MATH  MathSciNet  Google Scholar 

  9. Girish KP, John SJ (2011) Rough multisets and information multisystems. Adv Decis Sci. doi:10.1155/2011/495392.

  10. Girish KP, John SJ (2012) Multiset topologies induced by multiset relations. Inform Sci 188:298–313

    Article  MATH  MathSciNet  Google Scholar 

  11. Grzymala-Busse J (1987) Learning from examples based on rough multisets. In: Proceedings of the 2nd international symposium on methodologies for intelligent systems, Charlotte, NC, USA, pp 325-332

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

    Article  MathSciNet  Google Scholar 

  13. Jena SP, Ghosh SK, Tripathy BK (2001) On the theory of bags and lists. Inform Sci 132:241–254

    Article  MATH  MathSciNet  Google Scholar 

  14. Kondo M (2006) On the structure of generalized rough sets. Inform Sci 176:589-600

    Article  MATH  MathSciNet  Google Scholar 

  15. Kortelainen J (1994) On relationship between modified sets, topological spaces and rough sets. Fuzzy Sets Sys 61:91–95

    Article  MATH  MathSciNet  Google Scholar 

  16. Lashin E, Kozae A, Khadra AA, Medhat T (2005) Rough set theory for topological spaces. Int J Approx Reason 40(1-2): 35–43

    Google Scholar 

  17. Li X, Liu S (2012) Matroidal approaches to rough sets via closure operators. Int J Approx Reason 53(4):513–527

    Article  MATH  Google Scholar 

  18. Li Z, Xie T, Li Q (2012) Topological structure of generalized rough sets. Comput Math Appl 63:1066–1071

    Article  MATH  MathSciNet  Google Scholar 

  19. Li T-J, Yeung Y, Zhang W-X (2008) Generalized fuzzy rough approximation operators based on fuzzy covering. Int J Approx Reason 48:836–856

    Article  MATH  Google Scholar 

  20. Pawlak Z (1991) Rough sets: Theoretical aspects of reasoning about data. Kluwer Academic Publishers, Boston

  21. Pei D (2007) On definable concepts of rough set models. Inform Sci 177:4230–4239

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  23. Polkowski L (2001) On fractals defined in information systems via rough set theory. In: Proceedings of the RSTGC-2001, Bulletin International Rough Set Society 5 (1/2):163–166

  24. Polkowski L (2002) Rough sets: mathematical foundations. Physica-Verlag, Heidelberg

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

    Article  MATH  MathSciNet  Google Scholar 

  26. Skowron A (1988) On topology in information system. Bull Polish Acad Sci Math 36:477–480

    MATH  MathSciNet  Google Scholar 

  27. Skowron A, Stepaniuk J (1996) Tolerance approximation spaces. Fundamenta Informaticae 27:245–253

    MATH  MathSciNet  Google Scholar 

  28. Skowron A, Swiniarski R, Synak P (2005) Approximation spaces and information granulation. Trans Rough Sets III Lect Notes Comput Sci 3400:175–189

    Article  Google Scholar 

  29. Slowinski R, Vanderpooten D (2000) A generalized definition of rough approximations based on similarity. IEEE Trans Knowl Data Eng 12(2):331–336

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  31. Thuan ND (2009) Covering rough sets from a topological point of view. Int J Comput Theory Eng 1(5):1793–8201

    Google Scholar 

  32. Tversky A (1977) Features of similarity. Psychol Rev 84(4):327–352

    Article  Google Scholar 

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

    Google Scholar 

  34. Yager RR (1986) On the theory of bags. Int J Gen Sys 13:23–37

    Article  MathSciNet  Google Scholar 

  35. Yang X, Song Z, Chen Z, Yang J (2011) On multigranulation rough sets in incomplete information systems. Int J Mach Learn Cybern. doi:10.1007/s13042-011-0054-8

  36. Yang L, Xu L (2011) Topological properties of generalized approximation spaces. Inform Sci 181:3570–3580

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt

    E. A. Abo-Tabl

  2. Mathematics Department, Faculty of Science and Arts, Qassim University, Muthnab, Kingdom of Saudi Arabia

    E. A. Abo-Tabl

Authors
  1. E. A. Abo-Tabl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. A. Abo-Tabl.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abo-Tabl, E.A. Topological approaches to generalized definitions of rough multiset approximations. Int. J. Mach. Learn. & Cyber. 6, 399–407 (2015). https://doi.org/10.1007/s13042-013-0196-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-013-0196-y

Keywords

Search

Navigation