Skip to main content
Springer Nature Link
Log in

Rough Sets and Higher Order Vagueness

  • Conference paper
Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RSFDGrC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3641))

  • 1326 Accesses

Abstract

We present a rough set approach to vague concept approximation within the adaptive learning framework. In particular, the role of extensions of approximation spaces in searching for concept approximation is emphasized. Boundary regions of approximated concepts within the adaptive learning framework are satisfying the higher order vagueness condition, i.e., the boundary regions of vague concepts are not crisp. There are important consequences of the presented framework for research on adaptive approximation of vague concepts and reasoning about approximated concepts. An illustrative example is included showing the application of Boolean reasoning in adaptive learning.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Friedman, J., Hastie, T., Tibshirani, R.: The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  2. Keefe, R.: Theories of Vagueness. Cambridge Studies in Philosophy, Cambridge (2000)

    Google Scholar 

  3. Pavelka, J.: On Fuzzy Logic I-III. Zeit. Math Logik Grund. Math. 25, 45–52, 119-134, 447-464 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  4. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. In: System Theory, Knowledge Engineering and Problem Solving, vol. 9. Kluwer Academic Publishers, Dordrecht (1991)

    Google Scholar 

  5. Pawlak, Z., Skowron, A.: Rough Membership Functions. In: Yager, R.R., Fedrizzi, M., Kacprzyk, J. (eds.) Advances in the Dempster-Schafer Theory of Evidence, pp. 251–271. John Wiley and Sons, New York (1994)

    Google Scholar 

  6. Polkowski, L.: Rough Sets: Mathematical Foundations. Physica, Heidelberg (2002)

    MATH  Google Scholar 

  7. Polkowski, L., Skowron, A.: Rough Mereology: A New Paradigm for Approximate Reasoning. International Journal of Approximate Reasoning 15, 333–365 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  8. Read, S.: Thinking about Logic. An Introduction to the Philosophy of Logic. Oxford University Press, Oxford (1995)

    Google Scholar 

  9. Skowron, A.: Rough Sets in KDD. In: 16-th World Computer Congress (IFIP 2000), Beijing, August 19-25 (2000) In: Shi, Z., Faltings, B., Musen, M. (eds.) Proceedings of Conference on Intelligent Information Processing (IIP 2000), Beijing, pp. 1–17. ishing House of Electronic Industry, Beijing (2000)URL, 1

    Google Scholar 

  10. Skowron, A.: Rough Sets and Vague Concepts. Fundamenta Informaticae 4(1-4), 417–431 (2005)

    MathSciNet  Google Scholar 

  11. Skowron, A., Stepaniuk, J.: Tolerance Approximation Spaces. Fundamenta Informaticae 27, 245–253 (1996)

    MATH  MathSciNet  Google Scholar 

  12. Skowron, A., Stepaniuk, J.: Information Granules and Rough-Neural Computing. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough-Neural Computing: Techniques for Computing with Words, Cognitive Technologies, pp. 43–84. Springer, Heidelberg (2004)

    Google Scholar 

  13. Skowron, A., Swiniarski, R., Synak, P.: Approximation spaces and information granulation. In: Tsumoto, S., Słowiński, R., Komorowski, J., Grzymała-Busse, J.W. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 114–123. Springer, Heidelberg (2004)

    Google Scholar 

  14. Stone, P.: Layered Learning in Multi-Agent Systems: A Winning Approach to Robotic Soccer. The MIT Press, Cambridge (2000)

    Google Scholar 

  15. Suraj, Z.: The synthesis problem of concurrent systems specified by dynamic information systems. In: Polkowski, L., Skowron, A. (eds.) Rough Sets in Knowledge Discovery 2: Applications, Case Studies and Software Systems, pp. 418–448. Physica, Heidelberg (1998)

    Google Scholar 

  16. Sutton, R.S., Barto, A.G.: Reinforcement Learning: An Introduction. MIT Press, Cambridge (1998)

    Google Scholar 

  17. Vapnik, V.: Statistical Learning Theory. John Wiley & Sons, New York (1998)

    MATH  Google Scholar 

  18. Wojna, A.: Constraint based incremental learning of classification rules. In: Ziarko, W.P., Yao, Y. (eds.) RSCTC 2000. LNCS (LNAI), vol. 2005, pp. 428–435. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  19. Ziarko, W.: Variable Precision Rough Set Model. Journal of Computer and System Sciences 46, 39–59 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  20. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 333–353 (1965)

    Article  MathSciNet  Google Scholar 

  21. Zadeh, L.A.: Fuzzy Logic = Computing with Words. IEEE Transactions on Fuzzy Systems 2, 103–111 (1996)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Andrzej Skowron

  2. Institute of Computer Science, Polish Academy of Sciences, Ordona 21, 01-237, Warsaw, Poland

    Roman Swiniarski

  3. Department of Mathematical and Computer Sciences, San Diego State University, 5500 Campanile Drive, San Diego, CA, 92182, USA

    Roman Swiniarski

Authors
  1. Andrzej Skowron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roman Swiniarski
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Regina, Regina, SK, S4S 0A2 Canada, Polish-Japanese Institute of Information Technology, Koszykowa 86, 02-008 Warsaw, P.O. Box, Poland

    Dominik Ślęzak

  2. School of Information Science and Technology, Southwest Jiaotong University, 610031, Chengdu, P.R. China

    Guoyin Wang

  3. Institute of Mathematics, Warsaw University, Banacha 2, 02-097, Warsaw, Poland

    Marcin Szczuka

  4. Department of Computer Science, Brock University, St. Catharines, L2S 3A1, Ontario, Canada

    Ivo Düntsch

  5. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Skowron, A., Swiniarski, R. (2005). Rough Sets and Higher Order Vagueness. In: Ślęzak, D., Wang, G., Szczuka, M., Düntsch, I., Yao, Y. (eds) Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. RSFDGrC 2005. Lecture Notes in Computer Science(), vol 3641. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11548669_4

Download citation

  • DOI: https://doi.org/10.1007/11548669_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28653-0

  • Online ISBN: 978-3-540-31825-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics