Skip to main content

A Novel Approach to Roughness Measure in Fuzzy Rough Sets

  • Conference paper
Fuzzy Information and Engineering

Part of the book series: Advances in Soft Computing ((AINSC,volume 40))

Abstract

A hot topic of rough set theory is the combination of fuzzy set theory and this one. Many researchers do the work by introducing the concept of level fuzzy sets. In this paper, we will study roughness measure in fuzzy rough set in this way, too. The lower and the upper approximation based on λ-level fuzzy set will be proposed, and their properties be discussed. Moreover we introduced the new method to the roughness measure in fuzzy rough sets according to these concepts.

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 259.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
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. International Journal of Computer Information Sciences 11, 145–172 (1982)

    MathSciNet  Google Scholar 

  2. Pawlak, Z.: Rough Sets-Theoretical Aspects to Reasoning about Data. Kluwer Academic Publisher, Boston (1991)

    Google Scholar 

  3. Yao, Y.Y.: Combination of Rough and Fuzzy Sets Based on -Level Sets. In: Lin, T.Y., Cercone, N. (eds.) Rough Sets and Data Mining: Analysis for Imprecise Data, Kluwer Academic, Boston (1997)

    Google Scholar 

  4. 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 

  5. Yao, Y.Y., Lin, T.Y.: Generalization of Rough Sets Using Modal Logic. Intelligent Automation and Soft Computing, An International Journal 2, 103–120 (1996)

    Google Scholar 

  6. Zhang, W.X., et al.: Theory and Method of rough sets. Science Press, Beijing (2001)

    Google Scholar 

  7. Zhang, W.X., Liang, Y., Wu, W.Z.: Information Systems and Knowledge Discovery. Science Press, Beijing (2003)

    Google Scholar 

  8. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dubois, D., Prade, H.: Rough Fuzzy Sets and fuzzy Rough Sets. International Journal of General Systems 17, 191–208 (1990)

    Article  Google Scholar 

  10. Cornelis, C., Cock, M.D., Kerre, E.E.: Intuitionistic Fuzzy Rough Sets: At the Crossroads of Imperfect Knowledge. Expert Systems 20, 260–270 (2003)

    Article  Google Scholar 

  11. Radzikowska, A.M., Keere, E.E.: A Comparative Study Rough Sets. Fuzzy Sets and Systems 126, 137–156 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  12. Banerjee, M., Miltra, S., Pal, S.K.: Rough fuzzy MLP: knowledge encoding and classification. IEEE Trans. Neural Network 9, 1203–1216 (1998)

    Article  Google Scholar 

  13. Chakrabarty, K., Biswas, R., Nanda, S.: Fuzziness in Rough Sets. Fuzzy Set and Systems 110, 247–251 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. Mordeson, J.N.: Rough Sets Theory Applied to (Fuzzy) Ideal Theory. Fuzzy Sets and Systems 121, 315–324 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  15. Sarkar, M.: Rough-fuzzy Functions in Classification. Fuzzy Sets and Systems 132, 353–369 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  16. Baets, B.D., Kerre, E.: The Cutting of Compositions. Fuzzy Sets and Systems 62, 295–309 (1994)

    Article  MathSciNet  Google Scholar 

  17. Radecki, Z.: Level Fuzzy Sets. Journal of Cybernet. 7, 189–198 (1997)

    Article  MathSciNet  Google Scholar 

  18. Zenner, R.B.R.B., De Caluwe, R.M.M.: A New Approach to Information Retrieval Systems Using Fuzzy Expressions. Fuzzy Sets and Systems 17, 9–22 (1984)

    Google Scholar 

  19. Liu, W.N., Yao, J.T., Yao, Y.Y.: Rough Approximations under Level Fuzzy Sets. In: Tsumoto, S., et al. (eds.) RSCTC 2004. LNCS (LNAI), vol. 3066, pp. 78–83. Springer, Heidelberg (2004)

    Google Scholar 

  20. Banerjee, M., Pal, S.K.: Roughness of A Fuzzy Set. Information Sciences 1, 235–264 (1996)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Bing-Yuan Cao

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Zhang, Xy., Xu, Wh. (2007). A Novel Approach to Roughness Measure in Fuzzy Rough Sets. In: Cao, BY. (eds) Fuzzy Information and Engineering. Advances in Soft Computing, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71441-5_84

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-71441-5_84

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-71440-8

  • Online ISBN: 978-3-540-71441-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics