Skip to main content

A Comparison of Pawlak’s and Skowron–Stepaniuk’s Approximation of Concepts

  • Chapter
Transactions on Rough Sets VI

Part of the book series: Lecture Notes in Computer Science ((TRS,volume 4374))

Abstract

In this article, we compare mappings of Pawlak’s lower and upper approximations of concepts with those proposed by Skowron and Stepaniuk. It is known that both approaches coincide for the standard rough inclusion, so we consider the case of an arbitrary rough inclusion function. Even if the approximation space investigated is based on an arbitrary non-empty binary relation, the lower approximation mappings are equal in both approaches. Nevertheless, the upper approximation mappings are different in general.

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

Access this chapter

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

    Article  MathSciNet  Google Scholar 

  2. Pawlak, Z.: Information systems – Theoretical foundations. Information Systems 6, 205–218 (1981)

    Article  MATH  Google Scholar 

  3. Pawlak, Z.: Rough sets. Computer and Information Sciences 11, 341–356 (1982)

    Article  MathSciNet  Google Scholar 

  4. Pawlak, Z.: Information Systems. Theoretical Foundations (in Polish). Wydawnictwo Naukowo-Techniczne, Warsaw (1983)

    Google Scholar 

  5. Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning About Data. Kluwer, Dordrecht (1991)

    MATH  Google Scholar 

  6. Pomykała, J.A.: Approximation operations in approximation space. Bull. Polish Acad. Sci. Math. 35, 653–662 (1987)

    MathSciNet  Google Scholar 

  7. Wybraniec-Skardowska, U.: On a generalization of approximation space. Bull. Polish Acad. Sci. Math. 37, 51–62 (1989)

    MATH  MathSciNet  Google Scholar 

  8. Żakowski, W.: Approximations in the space (U,Π). Demonstratio Mathematica 16, 761–769 (1983)

    MathSciNet  Google Scholar 

  9. Skowron, A., Stepaniuk, J.: Generalized approximation spaces. In: Proc. 3rd Int. Workshop Rough Sets and Soft Computing, San Jose, USA, November 10-12, pp. 156–163 (1994)

    Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  11. Gomolińska, A.: Variable-precision compatibility spaces. Electronical Notices in Theoretical Computer Science 82, 1–12 (2003), http://www.elsevier.nl/locate/entcs/volume82.html

    Google Scholar 

  12. Słowiński, R., Vanderpooten, D.: Similarity relation as a basis for rough approximations. In: Wang, P.P. (ed.) Advances in Machine Intelligence and Soft Computing, vol. 4, pp. 17–33. Duke University Press, Durham (1997)

    Google Scholar 

  13. Yao, Y.Y., Wong, S.K.M., Lin, T.Y.: A review of rough set models. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis of Imprecise Data, pp. 47–75. Kluwer, Dordrecht (1997)

    Google Scholar 

  14. Ziarko, W.: Variable precision rough set model. J. Computer and System Sciences 46, 39–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Ziarko, W.: Probabilistic decision tables in the variable precision rough set model. J. Comput. Intelligence 17, 593–603 (2001)

    Article  Google Scholar 

  16. Peters, J.F.: Approximation space for intelligent system design patterns. Engineering Applications of Artificial Intelligence 17, 1–8 (2004)

    Article  Google Scholar 

  17. Skowron, A.: Approximation spaces in rough neurocomputing. In: Inuiguchi, M., Hirano, S., Tsumoto, S. (eds.) Rough Set Theory and Granular Computing. Studies in Fuzziness and Soft Computing, vol. 125, pp. 13–22. Springer, Heidelberg (2003)

    Google Scholar 

  18. Skowron, A., Swiniarski, R., Synak, P.: Approximation spaces and information granulation. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets III. LNCS, vol. 3400, pp. 175–189. Springer, Heidelberg (2005)

    Google Scholar 

  19. Polkowski, L., Skowron, A.: Rough mereology. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1994. LNCS, vol. 869, pp. 85–94. Springer, Heidelberg (1994)

    Google Scholar 

  20. Polkowski, L., Skowron, A.: Rough mereology: A new paradigm for approximate reasoning. Int. J. Approximated Reasoning 15, 333–365 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  21. Łukasiewicz, J.: Die logischen Grundlagen der Wahrscheinlichkeitsrechnung (First published in Kraków in 1913). In: Borkowski, L. (ed.) Jan Łukasiewicz – Selected Works, pp. 16–63. North Holland, Amsterdam (1970)

    Google Scholar 

  22. Zadeh, L.A.: Outline of a new approach to the analysis of complex system and decision processes. IEEE Trans. on Systems, Man, and Cybernetics 3, 28–44 (1973)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

James F. Peters Andrzej Skowron Ivo Düntsch Jerzy Grzymała-Busse Ewa Orłowska Lech Polkowski

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this chapter

Cite this chapter

Gomolińska, A. (2007). A Comparison of Pawlak’s and Skowron–Stepaniuk’s Approximation of Concepts. In: Peters, J.F., Skowron, A., Düntsch, I., Grzymała-Busse, J., Orłowska, E., Polkowski, L. (eds) Transactions on Rough Sets VI. Lecture Notes in Computer Science, vol 4374. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71200-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71200-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71198-8

  • Online ISBN: 978-3-540-71200-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics