Skip to main content
Springer Nature Link
Log in

Optimistic Multi-Granulation Fuzzy Rough Set Model Based on Triangular Norm

  • Conference paper
Rough Sets and Knowledge Technology (RSKT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7414))

Included in the following conference series:

Abstract

With granular computing point of view, the generalized T-fuzzy rough set model is based on a single fuzzy granulation in a T-fuzzy approximation space. This paper is devoted to the construction and study of the multi-granulation rough set based on triangular norm by defining the optimistic multi-granulation T-fuzzy lower and upper approximation operators in the generalized T-fuzzy approximation space. It is obvious that the generalize T-fuzzy lower and upper approximation operators defined on (U,R) are obtained as a special case of these operators. The main properties of the T-fuzzy lower and upper approximation operators are also studied.

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

Access this chapter

Log in via an institution

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

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.

Similar content being viewed by others

References

  1. Khan, M. A., Ma, M.: A Modal Logic for Multiple-Source Tolerance Approximation Spaces. In: Banerjee, M., Seth, A. (eds.) Logic and Its Applications. LNCS (LNAI), vol. 6521, pp. 124–136. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  2. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11(5), 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dubois, D., Prade, H.: Rough fuzzy sets and fuzzy rough sets. International Journal of General Systems 17, 191–208 (1990)

    Article  MATH  Google Scholar 

  4. Dubois, D., Prade, H.: Putting rough sets and fuzzy sets together (1992)

    Google Scholar 

  5. Zadeh, L.A.: Fuzzy Sets and Information Granularity, Advances in fuzzy set theory and application. North Holland Publishing, Amstandam (1979)

    Google Scholar 

  6. Qian, Y.H., Liang, J.Y., Dang, C.Y.: Knowledge structure, knowledge granulation and knowledge distance in a knowledge base. International Journal of Approximate Reasoning 50, 174–188 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Qian, Y.H., Liang, J.Y., Yao, Y.Y., Dang, C.H.: MGRS: A multi-granulation rough set. Information Sciences 180, 949–970 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Xu, W.H., Zhang, X.Y., Zhang, W.X.: Two new types of multiple granulation rough set. Information Sciences (submitted)

    Google Scholar 

  9. Xu, W.H., Zhang, X.T., Wang, Q.R.: A Generalized Multi-granulation Rough Set Approach. In: Huang, D.-S., Gan, Y., Premaratne, P., Han, K. (eds.) ICIC 2011. LNCS, vol. 6840, pp. 681–689. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  10. Xu, W.H., Wang, Q.R., Zhang, X.T.: Multi-granulation Fuzzy Rough Set Model on Tolerance Relations. In: Fourth International Workshop on Advanced Computational Intelligence, pp. 359-366 (2011)

    Google Scholar 

  11. Zhang, W.X., Wu, W.Z., Liang, J.Y., Li, D.Y.: Theory and method of rough sets (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing University of Technology, Chongqing, 400054, P.R. China

    Weihua Xu, Wenxin Sun & Yufeng Liu

Authors
  1. Weihua Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wenxin Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yufeng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

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

    Tianrui Li

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

    Hung Son Nguyen

  3. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, 400065, Chongqing, China

    Guoyin Wang

  4. Department of Electrical Engineering and Computer Science, University of Kansas, 66045 - 7621, Lawrence, KS, USA

    Jerzy Grzymala-Busse

  5. Department of Computing and Software, McMaster University, L8S 4K1, Hamilton, Ontario, Canada

    Ryszard Janicki

  6. Faculty of Computers and Information, Cairo University, Cairo, Egypt

    Aboul Ella Hassanien

  7. Software School, Dalian University of Technology, Dalian, China

    Hong Yu

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Xu, W., Sun, W., Liu, Y. (2012). Optimistic Multi-Granulation Fuzzy Rough Set Model Based on Triangular Norm. In: Li, T., et al. Rough Sets and Knowledge Technology. RSKT 2012. Lecture Notes in Computer Science(), vol 7414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31900-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31900-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31899-3

  • Online ISBN: 978-3-642-31900-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics