Skip to main content
SpringerLink
Log in

Interpreting Fuzzy Membership Functions in the Theory of Rough Sets

  • Conference paper
  • First Online:
Rough Sets and Current Trends in Computing (RSCTC 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2005))

Included in the following conference series:

Abstract

A fundamental difficulty with fuzzy set theory is the semantical interpretations of membership functions. We address this issue in the theory of rough sets. Rough membership functions are viewed as a special type of fuzzy membership functions interpretable using conditional probabilities. Rough set approximations are related to the core and support of a fuzzy set. A salient feature of the interpretation is that membership values of equivalent or similar elements are related to each other. Two types of similarities are considered, one is defined by a partition of the universe, and the other is denned by a covering.

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 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. D. Dubois and H. Prade, Similarity-based approximate reasoning, in: J. M. Zurada, R. J. Marks II, C. J. Robinson (Eds.), Computational Intelligence: Imitating Life, IEEE Press, New York, 69–80, 1994.

    Google Scholar 

  2. G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice Hall, New Jersey, 1995.

    MATH  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Y. Y. Yao, A comparative study of fuzzy sets and rough sets, Information Sciences, 109, 227–242, 1998.

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  8. L. A. Zadeh, Fuzzy sets, Information and Control, 8, 338–353, 1965.

    Article  MATH  MathSciNet  Google Scholar 

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

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Y. Y. Yao & J. P. Zhang

Authors
  1. Y. Y. Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. P. Zhang
    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, S4S 0A2, Saskatchewan, Canada

    Wojciech Ziarko  & Yiyu Yao  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yao, Y.Y., Zhang, J.P. (2001). Interpreting Fuzzy Membership Functions in the Theory of Rough Sets. In: Ziarko, W., Yao, Y. (eds) Rough Sets and Current Trends in Computing. RSCTC 2000. Lecture Notes in Computer Science(), vol 2005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45554-X_9

Download citation

  • DOI: https://doi.org/10.1007/3-540-45554-X_9

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43074-2

  • Online ISBN: 978-3-540-45554-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation