Skip to main content
SpringerLink
Log in

Covering Based Rough Sets and Relation Based Rough Sets

  • Conference paper
Rough Sets and Intelligent Systems Paradigms

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8537))

Abstract

Relation based rough sets and covering based rough sets are two important extensions of the classical rough sets. This paper investigates relationships between relation based rough sets and the covering based rough sets in a particular framework of approximation operators, presents a new group of approximation operators obtained by combining coverings and neighborhood operators and establishes some relationships between covering based rough sets and relation based rough sets.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bonikowski, Z., Brynarski, E.: Extensions and Intensions in rough set theory. Information Science 107, 149–167 (1998)

    Article  Google Scholar 

  2. Couso, I., Dubois, D.: Rough sets, coverings and incomplete information. Fundamenta Informaticae 108, 223–247 (2011)

    MathSciNet  MATH  Google Scholar 

  3. Dai, J.: Rough sets approach to incomplete numerical data. Information Sciences 214, 43–57 (2013)

    Article  MathSciNet  Google Scholar 

  4. Grzymala-Busse, J., Siddhaye, S.: Rough Sets approach to rule induction from incomplete data. In: Proceedings of 10th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 923–930 (2004)

    Google Scholar 

  5. Grzymała-Busse, J.W.: Data with Missing Attribute Values: Generalization of Indiscernibility Relation and Rule Induction. In: Peters, J.F., Skowron, A., Grzymała-Busse, J.W., Kostek, B., Swiniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets I. LNCS, vol. 3100, pp. 78–95. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  6. Järvinen, J.: Lattice Theory for Rough Sets. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds.) Transactions on Rough Sets VI. LNCS, vol. 4374, pp. 400–498. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Järvinen, J., Radeleczki, S.: Rough Sets determined by tolerance. International Journal of Approximate Reasoning (2013), http://dx.doi.org/10.1016/j.ijar.2013.12.005

  8. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  Google Scholar 

  9. Restrepo, M., Cornelis, C., Gómez, J.: Duality, Conjugacy and Adjointness of Approximation Operators in Covering-based Rough Sets. International Journal of Approximate Reasoning 55, 469–485 (2014)

    Article  MathSciNet  Google Scholar 

  10. Samanta, P., Chakraborty, M.K.: Covering based approaches to rough sets and implication lattices. In: Sakai, H., Chakraborty, M.K., Hassanien, A.E., Ślęzak, D., Zhu, W. (eds.) RSFDGrC 2009. LNCS (LNAI), vol. 5908, pp. 127–134. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  11. Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces. Fundamenta Informaticae 55, 245–253 (1996)

    MathSciNet  MATH  Google Scholar 

  12. Slowinski, R., Venderpooten, D.: A generalized definition of rough approximation based on similarity. IEEE Transaction on Knowledge and Data Engineering 12, 331–336 (2000)

    Article  Google Scholar 

  13. Wu, M., Wu, X., Shen, T.: A New Type of Covering Approximation Operators. In: International Conference on Electronic Computer Technology, pp. 334–338. IEEE (2009)

    Google Scholar 

  14. Xu, W., Zhang, W.: Measuring roughness of generalized rough sets induced by a covering. Fuzzy Sets and Systems 158, 2443–2455 (2007)

    Article  MathSciNet  Google Scholar 

  15. Yang, T., Li, Q.: Reduction about Approximation Spaces of Covering Generalized Rough Sets. International Journal of Approximate Reasoning 51, 335–345 (2010)

    Article  MathSciNet  Google Scholar 

  16. Yao, Y.Y.: Constructive and Algebraic Methods of the Theory of Rough Sets. Information Sciences 109, 21–47 (1998)

    Article  MathSciNet  Google Scholar 

  17. Yao, Y.Y.: Generalized Rough Sets Models. In: Polkowski, L., Skowron, A. (eds.) Knowledge Discovery, pp. 286–318. Physica-Verlag (1998)

    Google Scholar 

  18. Yao, Y.Y.: On generalizing Rough Sets Theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds.) RSFDGrC 2003. LNCS (LNAI), vol. 2639, pp. 44–51. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  19. Yao, Y.Y., Yao, B.: Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning 15, 299–317 (1996)

    Article  MathSciNet  Google Scholar 

  20. Yao, Y.Y., Yao, B.: Covering Based Rough Sets Approximations. Information Sciences 200, 91–107 (2012)

    Article  MathSciNet  Google Scholar 

  21. Zakowski, W.: Approximations in the Space (u,π). Demonstratio Mathematica 16, 761–769 (1983)

    Article  MathSciNet  Google Scholar 

  22. Zhang, Y.L., Li, J., Wu, W.: On Axiomatic Characterizations of Three Pairs of Covering Based Approximation Operators. Information Sciences 180, 274–287 (2010)

    Article  MathSciNet  Google Scholar 

  23. Zhang, Y.L., Luo, M.K.: Relationships between covering-based rough sets and relation-based rough sets. Information Sciences 225, 55–71 (2013)

    Article  MathSciNet  Google Scholar 

  24. Zhu, W.: Basics concepts in Covering-Based Rough Sets. In: Third International Conference on Natural Computation, vol. 5, pp. 283–286 (2007)

    Google Scholar 

  25. Zhu, W.: Properties of the First Type of Covering-Based Rough Sets. In: Proceedings of Sixth IEEE International Conference on Data Mining - Workshops, pp. 407–411 (2006)

    Google Scholar 

  26. Zhu, W.: Properties of the Second Type of Covering-Based Rough Sets. In: Proceedings of the IEEE/WIC/ACM International Conference on Web Intelligence and Intelligent Agent Technology, pp. 494–497 (2006)

    Google Scholar 

  27. Zhu, W.: Properties of the Third Type of Covering-Based Rough Sets. In: Proceedings of International Conference on Machine Learning and Cybernetics, pp. 3746–3751 (2007)

    Google Scholar 

  28. Zhu, W.: Properties of the Fourth Type of Covering-Based Rough Sets. In: Proceedings of Sixth International Conference on Hybrid Intelligence Systems, p. 43 (2006)

    Google Scholar 

  29. Zhu, W., Wang, F.: On Three Types of Covering Based Rough Sets. IEEE Transactions on Knowledge and Data Engineering 19, 1131–1144 (2007)

    Article  Google Scholar 

  30. Zhu, W.: Relationship Between Generalized Rough Sets Based on Binary Relation and Covering. Information Sciences 179, 210–225 (2009)

    Article  MathSciNet  Google Scholar 

  31. Zhu, W., Wang, F.: A New Type of Covering Rough Set. In: Proceedings of Third International IEEE Conference on Intelligence Systems, pp. 444–449 (2006)

    Google Scholar 

  32. Zhu, W., Wang, F.: Reduction and Axiomatization of Covering Generalized Rough Sets. Information Sciences 152, 217–230 (2003)

    Article  MathSciNet  Google Scholar 

  33. Zhu, W., Wang, F.-Y.: Binary relation based Rough Sets. In: Wang, L., Jiao, L., Shi, G., Li, X., Liu, J. (eds.) FSKD 2006. LNCS (LNAI), vol. 4223, pp. 276–285. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universidad Nacional de Colombia, Bogotá, Colombia

    Mauricio Restrepo & Jonatan Gómez

Authors
  1. Mauricio Restrepo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jonatan Gómez
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Computer Science, Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland

    Marzena Kryszkiewicz  & Zbigniew W. Raś  & 

  2. Department of Computer Science and Artificial Intelligence, University of Granada, Calle del Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    Chris Cornelis

  3. DISCo, Università di Milano – Bicocca, Viale Sarca 336 – U14, 20126, Milano, Italy

    Davide Ciucci

  4. Dpt. de Matemáticas, University of Càdiz, Spain

    Jesús Medina-Moreno

  5. School of Computing and Information Systems, University of Tasmania, Japan

    Hiroshi Motoda

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Restrepo, M., Gómez, J. (2014). Covering Based Rough Sets and Relation Based Rough Sets. In: Kryszkiewicz, M., Cornelis, C., Ciucci, D., Medina-Moreno, J., Motoda, H., Raś, Z.W. (eds) Rough Sets and Intelligent Systems Paradigms. Lecture Notes in Computer Science(), vol 8537. Springer, Cham. https://doi.org/10.1007/978-3-319-08729-0_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08729-0_13

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08728-3

  • Online ISBN: 978-3-319-08729-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation