Skip to main content

On Generalizing Rough Set Theory

  • Conference paper
  • First Online:
Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2639))

Abstract

This paper summarizes various formulations of the standard rough set theory. It demonstrates how those formulations can be adopted to develop different generalized rough set theories. The relationships between rough set theory and other theories are discussed.

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

Access this chapter

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

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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. Cattaneo, G. Abstract approximation spaces for rough theories, in: Rough Sets in Knowledge Discovery, Polkowski, L. and Skowron, A. (Eds.), Physica-Verlag, Heidelberg, 59–98, 1998.

    Google Scholar 

  2. Chellas, B.F. Modal Logic: An Introduction, Cambridge University Press, Cambridge, 1980.

    MATH  Google Scholar 

  3. Cohn, P.M. Universal Algebra, Harper and Row Publishers, New York, 1965.

    MATH  Google Scholar 

  4. Järvinen, J. On the structure of rough approximations, Proceedings of the Third International Conference on Rough Sets and Current Trends in Computing, LNAI 2475, 123–130, 2002.

    Google Scholar 

  5. Lin, T.Y. and Liu, Q. Rough approximate operators: axiomatic rough set theory, in Rough Sets, Fuzzy Sets and Knowledge Discovery, W.P. Ziarko (Ed.), Springer-Verlag, London, 256–260, 1994.

    Google Scholar 

  6. Pawlak, Z. Rough sets, International Journal of Computer and Information Sciences, 11, 341–356, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  7. Pawlak, Z. Rough Sets: Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, Boston, 1991.

    MATH  Google Scholar 

  8. Pawlak, Z. and Skowron, A. Rough membership functions, in: Advances in the Dempster-Shafer Theory of Evidence, Yager, R.R., Fedrizzi, M. and Kacprzyk, J. (Eds.), John Wiley and Sons, New York, 251–271, 1994.

    Google Scholar 

  9. Pomykala, J.A. Approximation operations in approximation space, Bulletin of Polish Academy of Sciences, Mathematics, 35, 653–662, 1987.

    MATH  MathSciNet  Google Scholar 

  10. Rasiowa, H. An Algebraic Approach to Non-classical Logics, North-Holland, Amsterdam, 1974.

    MATH  Google Scholar 

  11. Skowron, A. and Grzymala-Busse, J. From rough set theory to evidence theory, in: Advances in the Dempster-Shafer Theory of Evidence, Yager, R.R., Fedrizzi, M. and Kacprzyk, J. (Eds.), Wiley, New York, 193–236, 1994.

    Google Scholar 

  12. Wiweger, A. On topological rough sets, Bulletin of the Polish Academy of Sciences, Mathematics, 37, 89–93, 1989.

    MATH  MathSciNet  Google Scholar 

  13. Wong, S.K.M. and Ziarko, W. Comparison of the probabilistic approximate classification and the fuzzy set model, Fuzzy Sets and Systems, 21, 357–362, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  14. Wybraniec-Skardowska, U. On a generalization of approximation space, Bulletin of the Polish Academy of Sciences, Mathematics, 37, 51–61, 1989.

    MATH  MathSciNet  Google Scholar 

  15. Wybraniec-Skardowska, U. Unit Operations, ZeszytyNaukowe Wyzszej Szkoly Pedagogicznej im Powstancow Slaskich w Opolu, Matematyka, XXVII, 113–129, 1992.

    MathSciNet  Google Scholar 

  16. Yao, Y.Y. Two views of the theory of rough sets in finite universes, International Journal of Approximation Reasoning, 15, 291–317, 1996.

    Article  MATH  Google Scholar 

  17. Yao, Y.Y. Constructive and algebraic methods of the theory of rough sets, Information Sciences, 109, 21–47, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  18. Yao, Y.Y. Generalized rough set models, in: Rough Sets in Knowledge Discovery, Polkowski, L. and Skowron, A. (Eds.), Physica-Verlag, Heidelberg, 286–318, 1998.

    Google Scholar 

  19. Yao, Y.Y. Relational interpretations of neighborhood operators and rough set approximation operators, Information Sciences, 111, 239–259, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  20. Yao, Y.Y. On generalizing Pawlak approximation operators, Proceedings of the First International Conference, RSCTC’98, LNAI 1424, 298–307, 1998.

    Google Scholar 

  21. Yao, Y.Y. Information granulation and rough set approximation, International Journal of Intelligent Systems, 16, 87–104, 2001.

    Article  MATH  Google Scholar 

  22. Yao, Y.Y. Information granulation and approximation in a decision-theoretic model of rough sets, manuscript, 2002.

    Google Scholar 

  23. Yao, Y.Y. Probabilistic approaches to rough sets, manuscript, 2002.

    Google Scholar 

  24. Yao, Y.Y. Semantics of fuzzy sets in rough set theory, manuscript, 2002.

    Google Scholar 

  25. Yao, Y.Y. and Lin, T.Y. Generalization of rough sets using modal logic, Intelligent Automation and Soft Computing, An International Journal, 2, 103–120, 1996.

    Google Scholar 

  26. Yao, Y.Y. and Lingras, P.J. Interpretations of belief functions in the theory of rough sets, Information Sciences, 104, 81–106, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  27. Yao, Y.Y. and Wang, T. On rough relations: an alternative formulation, Proceedings of The Seventh International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, LNAI 1711, 82–90, 1999.

    Google Scholar 

  28. Yao, Y.Y. and Wong, S.K.M. A decision theoretic framework for approximating concepts, International Journal of Man-machine Studies, 37, 793–809, 1992.

    Article  Google Scholar 

  29. Yao, Y.Y., Wong, S.K.M. and Lin, T.Y. A review of rough set models, in: Rough Sets and Data Mining: Analysis for Imprecise Data, Lin, T.Y. and Cercone, N. (Eds.), Kluwer Academic Publishers, Boston, 47–75, 1997.

    Google Scholar 

  30. Zakowski, W. Approximations in the space (U, II), Demonstratio Mathematica, XVI, 761–769, 1983.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yao, Y.Y. (2003). On Generalizing Rough Set Theory. In: Wang, G., Liu, Q., Yao, Y., Skowron, A. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2003. Lecture Notes in Computer Science(), vol 2639. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-39205-X_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-39205-X_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-14040-5

  • Online ISBN: 978-3-540-39205-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics