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On the Intuitionistic Fuzzy Sets of n-th Type

  • Krassimir T. Atanassov
  • Peter Vassilev
Chapter
Part of the Studies in Computational Intelligence book series (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.

Notes

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”.

References

  1. 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. 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. 3.
    Atanassov, K.: A second type of intuitionistic fuzzy sets. BUSEFAL 56, 66–70 (1993)Google Scholar
  4. 4.
    Atanassov, K.: Intuitionistic fuzzy sets. Springer, Heidelberg (1999)Google Scholar
  5. 5.
    Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Heidelberg (2012)Google Scholar
  6. 6.
    Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy. Sets. Syst. 79(3), 403–405 (1996)Google Scholar
  7. 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. 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. 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. 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. 11.
    Gau, W.L., Buehrer, D.J.: Vague sets. IEEE. Trans. Syst. Man. Cybern. 23, 610–614 (1993)CrossRefMATHGoogle Scholar
  12. 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. 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. 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. 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. 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. 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)MATHGoogle Scholar
  18. 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. 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. 20.
    Ren, P., Xu, Z., Gou, X.: Pythagorean fuzzy TODIM approach to multi-criteria decision making. J. Appl. Soft. Comput. 42, 246–259 (2016)CrossRefGoogle Scholar
  21. 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. 22.
    Takeuti, G., Titani, S.: Intuitionistic fuzzy logic and intuitionistic fuzzy set theory. J. Symb. Log. 49(3), 851–866 (1984)Google Scholar
  23. 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. 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. 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. 26.
    Yager, R.R.: Pythagorean membership grades in multi-criteria decision making. IEEE Trans. Fuzzy Syst. 22, 958–965 (2014)CrossRefGoogle Scholar
  27. 27.
    Yager, R.R.: Properties and applications of Pythagorean fuzzy sets. Stud. Fuzziness. Soft. Comput. 332, 119–136 (2016)Google Scholar
  28. 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. 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. 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. 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

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of SciencesSofiaBulgaria
  2. 2.Intelligent Systems LaboratoryAsen Zlatarov UniversityBourgasBulgaria

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