Skip to main content

On the Intuitionistic Fuzzy Sets of n-th Type

  • Chapter
  • First Online:
Book cover Advances in Data Analysis with Computational Intelligence Methods

Part of the book series: Studies in Computational Intelligence ((SCI,volume 738))

Abstract

A survey and new results, related to the intuitionistic fuzzy sets of n-th type are given. Some open problems are formulated.

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 84.99
Price excludes VAT (USA)
  • Available as EPUB and 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
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. Atanassov K.: Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci.—Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulg.). Reprinted in: Int. J. Bioautomation, Vol. 20(S1), 2016, S1-S6 (in English)

    Google Scholar 

  2. Atanassov K.: Geometrical interpretations of the elements of the intuitionistic fuzzy objects. Preprint IM-MFAIS, 1–89. Sofia (1989). Reprinted in: Int. J. Bioautomation. 20(S1), S27–S42 (2016)

    Google Scholar 

  3. Atanassov, K.: A second type of intuitionistic fuzzy sets. BUSEFAL 56, 66–70 (1993)

    Google Scholar 

  4. Atanassov, K.: Intuitionistic fuzzy sets. Springer, Heidelberg (1999)

    Google Scholar 

  5. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Heidelberg (2012)

    Google Scholar 

  6. Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy. Sets. Syst. 79(3), 403–405 (1996)

    Google Scholar 

  7. Dick, S., Yager, R., Yazdanbakhsh, O.: On Pythagorean and complex fuzzy set operations. IEEE Trans. Fuzzy. Syst. 24(5), 1009–1021 (2016)

    Google Scholar 

  8. Garg, H.: A novel correlation coefficients between Pythagorean fuzzy sets and its applications to decision-making processes. Int. J. Intell. Syst. 31(12), 1234–1252 (2016)

    Google Scholar 

  9. Garg, H.: A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. Int. J. Intell. Syst. 31(9), 886–920 (2016)

    Google Scholar 

  10. Garg, H.: A novel accuracy function under interval-valued pythagorean fuzzy environment for solving multicriteria decision making problem. J. Intell. Fuzzy. Syst. 31(1), 529–540 (2016)

    Google Scholar 

  11. Gau, W.L., Buehrer, D.J.: Vague sets. IEEE. Trans. Syst. Man. Cybern. 23, 610–614 (1993)

    Article  MATH  Google Scholar 

  12. Gou, X., Xu, Z., Ren, P.: The properties of continuous Pythagorean fuzzy information. Int. J. Intell. Syst. 31(5), 401–424 (2016)

    Google Scholar 

  13. Liu, J., Zeng, S., Pan, T.: Pythagorean fuzzy dependent ordered weighted averaging operator and its application to multiple attribute decision making. Gummi. Fasern. Kunststoffe. 69(14), 2036–2042 (2016)

    Google Scholar 

  14. Ma, Z., Xu, Z.: Symmetric pythagorean fuzzy weighted geometric/averaging operators and their application in multicriteria decision-making problems. Int. J. Intell. Syst. 31(12), 1198–1219 (2016)

    Google Scholar 

  15. Palaniappan, N., Srinivasan, R.: Applications of intuitionistic fuzzy sets of root type in image processing. In: North American Fuzzy Information Processing Society (NAFIPS). Annual Conference (2009)

    Google Scholar 

  16. Palaniapan, N., Srinivasan, R., Parvathi, R.: Some operations on intuitionistic fuzzy sets of root type. Notes. Intuit. Fuzzy Sets. 12(3), 20–29 (2006)

    Google Scholar 

  17. Vassilev, P., Parvathi, R., Atanassov, K.: Note on intuitionistic fuzzy sets of \(p\)-th type. Issues. Intuit. Fuzzy Sets. Gener. Nets. 6, 43–50 (2008)

    MATH  Google Scholar 

  18. Peng, X., Yang, Y.: Fundamental properties of interval-valued pythagorean fuzzy aggregation operators. Int. J. Intell. Syst. 31(5), 444–487 (2016)

    Google Scholar 

  19. Peng, X., Yang, Y.: Pythagorean fuzzy Choquet integral based MABAC method for multiple attribute group decision making. Int. J. Intell. Syst. 31(10), 989–1020 (2016)

    Google Scholar 

  20. Ren, P., Xu, Z., Gou, X.: Pythagorean fuzzy TODIM approach to multi-criteria decision making. J. Appl. Soft. Comput. 42, 246–259 (2016)

    Article  Google Scholar 

  21. Srinivasan, R., Begum, S.S.: Some properties on intuitionistic fuzzy sets of third type. Ann. Fuzzy Math. Inform. 10(5), 799–804 (2015)

    Google Scholar 

  22. Takeuti, G., Titani, S.: Intuitionistic fuzzy logic and intuitionistic fuzzy set theory. J. Symb. Log. 49(3), 851–866 (1984)

    Google Scholar 

  23. Vassilev, P.: The generalized modal operator \(F^p_{\alpha ,\beta }\) over \(p\)-intuitionistic fuzzy sets. Notes. Intuit. Fuzzy. Sets. 15(4), 19–24 (2009)

    Google Scholar 

  24. Vassilev, P.: Intuitionistic fuzzy sets with membership and non-membership functions in metric relation, Ph.D. thesis defended on 18.03.2013, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences (in Bulgarian)

    Google Scholar 

  25. Vassilev, P.: Intuitionistic fuzzy sets generated by Archimedean metrics and ultrametrics. In: Recent Contributions in Intelligent Systems, Studies in Computational Intelligence 657, pp. 339–378 Springer, Cham (2017)

    Google Scholar 

  26. Yager, R.R.: Pythagorean membership grades in multi-criteria decision making. IEEE Trans. Fuzzy Syst. 22, 958–965 (2014)

    Article  Google Scholar 

  27. Yager, R.R.: Properties and applications of Pythagorean fuzzy sets. Stud. Fuzziness. Soft. Comput. 332, 119–136 (2016)

    Google Scholar 

  28. Zeng, S., Chen, J., Li, X.: A hybrid method for Pythagorean fuzzy multiple-criteria decision making. Int. J. Inf. Technol. Decis. Mak. 15(2), 403–422 (2016)

    Google Scholar 

  29. Zhang, C., Li, D., Ren, R.: Pythagorean fuzzy multigranulation rough set over two universes and its applications in merger and acquisition. Int. J. Intell. Syst. 31(9), 921–943 (2016)

    Google Scholar 

  30. Zhang, X.: A Novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int. J. Intell. Syst. 31(6), 593–611 (2016)

    Google Scholar 

  31. Zhang, X.: Multicriteria Pthagorean fuzzy decision analysis: a hierarchical QUALIFLEX approach with the closeness index-based ranking methods. Inf. Sci. 330, 104–124 (2016)

    Google Scholar 

Download references

Acknowledgements

The authors are thankful for the support provided by the Bulgarian National Science Fund under Grant Ref. No. DFNI-I-02-5 “InterCriteria Analysis: A New Approach to Decision Making”.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Krassimir T. Atanassov .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Cite this chapter

Atanassov, K.T., Vassilev, P. (2018). On the Intuitionistic Fuzzy Sets of n-th Type. In: Gawęda, A., Kacprzyk, J., Rutkowski, L., Yen, G. (eds) Advances in Data Analysis with Computational Intelligence Methods. Studies in Computational Intelligence, vol 738. Springer, Cham. https://doi.org/10.1007/978-3-319-67946-4_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-67946-4_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67945-7

  • Online ISBN: 978-3-319-67946-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics