Skip to main content
Log in

\(\boldsymbol{q}\)-Rung Orthopair Fuzzy Topological Spaces

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

The concept of \(q\)-rung orthopair fuzzy set is the extension of the concept of both intuitionistic fuzzy set and Pythagorean fuzzy set. The aim of this paper is to define the concept of \(q\)-rung orthopair fuzzy topological space and to study some properties of this concept. For this purpose, firstly the basic definition of \(q\)-rung orthopair fuzzy topology is introduced and an example is constructed and then the concept of \(q\)-rung orthopair fuzzy continuity is studied and it is shown that a \(q\)-rung orthopair fuzzy topology can be established on the domain or range of a function.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1

Similar content being viewed by others

REFERENCES

  1. K. T. Atanassov, ‘‘Intuitionistic fuzzy sets,’’ Fuzzy Sets Syst. 20, 87–96 (1986).

    Article  Google Scholar 

  2. R. E. Bellman and L. A. Zadeh, ‘‘Decision-making in a fuzzy environment,’’ Manage. Sci. 17, B141–B164 (1970).

    Article  MathSciNet  Google Scholar 

  3. N. Bourbaki, General Topology (Springer, Berlin, Heidelberg, 1995).

    Book  Google Scholar 

  4. C. L. Chang, ‘‘Fuzzy topological spaces,’’ J. Math. Anal. Appl. 24, 182–190 (1968).

    Article  MathSciNet  Google Scholar 

  5. D. Çoker, ‘‘An introduction to intuitionistic fuzzy topological spaces,’’ Fuzzy Sets Syst. 88, 81–89 (1997).

    Article  MathSciNet  Google Scholar 

  6. C. Hofer, R. Kwitt, M. Niethammer, and A. Uhl, ‘‘Deep learning with topological signatures,’’ Adv. Neural Inf. Process Syst. 30, 1634–1644 (2017).

    Google Scholar 

  7. L. Li, W. Y. Cheng, B. S. Glicksberg, O. Gottesman, R. Tamler, R. Chen, E. P. Bottinger, and J. T. Dudley, ‘‘Identification of type 2 diabetes subgroups through topological analysis of patient similarity,’’ Sci. Transl. Med. 7 (311), 311ra174 (2015).

  8. P. Y. Lum, G. Singh, A. Lehman, T. Ishkanov, M. Vejdemo-Johansson, M. Alagappan, J. Carlsson, and G. Carlsson, ‘‘Extracting insights from the shape of complex data using topology,’’ Sci. Rep. 3, 1236 (2013).

    Article  Google Scholar 

  9. M. Nicolau, A. J. Levine, and G. Carlsson, ‘‘Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival,’’ Proc. Natl. Acad. Sci. U. S. A. 108, 7265–7270 (2011).

    Article  Google Scholar 

  10. M. Olgun and M. Ünver, Ş Yardımcı, ‘‘Pythagorean fuzzy topological spaces,’’ Complex Intell. Syst. 5, 177–183 (2019).

    Article  Google Scholar 

  11. M. E. Sardiu, J. M. Gilmore, B. Groppe, L. Florens, and M. P. Washburn, ‘‘Identification of topological network modules in perturbed protein interaction networks,’’ Sci. Rep. 7, 43845 (2017).

    Article  Google Scholar 

  12. E. Witten, ‘‘Reflections on the fate of spacetime,’’ Phys. Today 96 (4), 24–30 (1996).

    Article  MathSciNet  Google Scholar 

  13. R. R. Yager, ‘‘Pythagorean fuzzy subsets,’’ in Proceedings of the 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), Edmonton, Canada, June 24–28, 2013 (IEEE, 2013), pp. 57–61.

  14. R. R. Yager, ‘‘Generalized orthopair fuzzy sets,’’ IEEE Trans. Fuzzy Syst. 25, 1222–1230 (2017).

    Article  Google Scholar 

  15. L. A. Zadeh, ‘‘Fuzzy sets,’’ Inf. Control 8, 338–353 (1965).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Ezgi Türkarslan, Mehmet Ünver or Murat Olgun.

Additional information

(Submitted by A. I. Volodin)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Türkarslan, E., Ünver, M. & Olgun, M. \(\boldsymbol{q}\)-Rung Orthopair Fuzzy Topological Spaces. Lobachevskii J Math 42, 470–478 (2021). https://doi.org/10.1134/S1995080221020219

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080221020219

Keywords:

Navigation