Skip to main content
SpringerLink
Log in

Intuitionistic Fuzzy Topologies in Crisp Approximation Spaces

  • 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:

  • 1525 Accesses

Abstract

A rough intuitionistic fuzzy set is the result of approximation of an intuitionistic fuzzy set with respect to a crisp approximation space. In this paper, we investigate topological structures of rough intuitionistic fuzzy sets. We examine that a reflexive crisp rough approximation space can induce an intuitionistic fuzzy Alexandrov space. It is proved that the lower and upper rough intuitionistic fuzzy approximation operators are, respectively, an intuitionistic fuzzy interior operator and an intuitionistic fuzzy closure operator if and only if the binary relation in the crisp approximation space is reflexive and transitive. Finally, we show that a similarity crisp approximation space can produce an intuitionistic fuzzy clopen topological space.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

Similar content being viewed by others

References

  1. Arenas, F.G.: Alexandroff Spaces. Acta Mathematica Universitatis Comenianae 68, 17–25 (1999)

    MathSciNet  MATH  Google Scholar 

  2. Atanassov, K.: Intuitionistic Fuzzy Sets. Physica-Verlag, Heidelberg (1999)

    MATH  Google Scholar 

  3. Boixader, D., Jacas, J., Recasens, J.: Upper and Lower Approximations of Fuzzy Sets. International Journal of General Systems 29, 555–568 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  4. Chang, C.L.: Fuzzy Topological Spaces. Journal of Mathematical Analysis and Applications 24, 182–189 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chuchro, M.: On Rough Sets in Topological Boolean Algebras. In: Ziarko, W. (ed.) Rough Sets, Fuzzy Sets and Knowledge Discovery, pp. 157–160. Springer, Berlin (1994)

    Chapter  Google Scholar 

  6. Coker, D.: An Introduction of Intuitionistic Fuzzy Topological spaces. Fuzzy Sets and Systems 88, 81–89 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication in Intuitionistic Fuzzy and Interval-valued Fuzzy Set Theory: Construction, Classification, Application. International Journal of Approximate Reasoning 35, 55–95 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kondo, M.: On the Structure of Generalized Rough Sets. Information Sciences 176, 589–600 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  9. Lai, H., Zhang, D.: Fuzzy Preorder and Fuzzy Topology. Fuzzy Sets and Systems 157, 1865–1885 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lashin, E.F., Kozae, A.M., Khadra, A.A.A., et al.: Rough Set Theory for Topological Spaces. International Journal of Approximate Reasoning 40, 35–43 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  11. Lowen, R.: Fuzzy Topological Spaces and Fuzzy Compactness. Journal of Mathematical Analysis and Applications 56, 621–633 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning about Data. Kluwer Academic Publishers, Boston (1991)

    MATH  Google Scholar 

  13. Qin, K.Y., Pei, Z.: On the Topological Properties of Fuzzy Rough Sets. Fuzzy Sets and Systems 151, 601–613 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Qin, K.Y., Yang, J., Pei, Z.: Generalized Rough Sets Based on Reflexive and Transitive Relations. Information Sciences 178, 4138–4141 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wiweger, R.: On Topological Rough Sets. Bulletin of Polish Academy of Sciences: Mathematics 37, 89–93 (1989)

    MathSciNet  MATH  Google Scholar 

  16. Wu, W.-Z., Xu, Y.-H.: Rough Approximations of Intuitionistic Fuzzy Sets in Crisp Approximation Spaces. In: Proceedings of Seventh International Conference onFuzzy Systems and Knowledge Discovery (FSKD 2010), vol. 1, pp. 309–313 (2010)

    Google Scholar 

  17. Wu, W.-Z., Yang, Y.-F., Xu, Y.-H.: Some Fuzzy Topologies Induced by Rough Fuzzy Sets. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds.) RSKT 2011. LNCS, vol. 6954, pp. 156–165. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  18. Wu, W.-Z., Zhou, L.: On Intuitionistic Fuzzy Topologies Based on Intuitionistic Fuzzy Reflexive and Transitive Relations. Soft Computing 15(6), 1183–1194 (2011)

    Article  MATH  Google Scholar 

  19. Yao, Y.Y.: Constructive and Algebraic Methods of the Theory of Rough Sets. Journal of Information Sciences 109, 21–47 (1998)

    Article  MATH  Google Scholar 

  20. Zhang, H.-P., Yao, O.Y., Wang, Z.D.: Note on Generlaized Rough Sets Based on Reflexive and Transitive Relations. Information Sciences 179, 471–473 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhou, L., Wu, W.-Z., Zhang, W.-X.: On Intuitionistic Fuzzy Rough Sets and Their Topological Structures. International Journal of General Systems 38, 589–616 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhu, W.: Topological Approaches to Covering Rough Sets. Information Sciences 177, 1499–1508 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, Zhejiang, 316004, P.R. China

    You-Hong Xu & Wei-Zhi Wu

Authors
  1. You-Hong Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei-Zhi Wu
    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, YH., Wu, WZ. (2012). Intuitionistic Fuzzy Topologies in Crisp Approximation Spaces. 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_61

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-31900-6_61

  • 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

Search

Navigation