Two Intuitionistic Fuzzy Modal-Level Operators

  • Krassimir T. AtanassovEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)


Two new intuitionistic fuzzy operators are introduced. For them it is shown that they have a behaviour similar both to the modal, as well as to the level operators, defined over intuitionistic fuzzy sets and for this reason, they are called intuitionistic fuzzy modal-level operators. Their basic properties are discussed.


Intuitionistic fuzzy set Intuitionistic fuzzy operator 



The present research has been supported by the Bulgarian National Science Fund under Grant Ref. No. DFNI-I-02-5 “InterCriteria Analysis: A New Approach to Decision Making”.


  1. 1.
    Atanassov, K.: Intuitionistic fuzzy sets. In: VII ITKR’s Session, Sofia, June 1983. (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulg.), Reprinted: Int. J. Bioautom. 20(S1), S1–S6 (2016)Google Scholar
  2. 2.
    Atanassov, K.: A universal operator over intuitionistic fuzzy sets. Comput. Rend. Acad. Bulg. Sci. Tome 46(1), 13–15 (1993)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Atanassov, K.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  4. 4.
    Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)CrossRefzbMATHGoogle Scholar
  5. 5.
    Atanassov, K.: A short remark on intuitionistic fuzzy operators \(X_{a, b, c, d, e, f}\) and \(x_{a, b, c, d, e, f}\). Notes Intuitionistic Fuzzy Sets 19(1), 54–56 (2013)MathSciNetGoogle Scholar
  6. 6.
    Atanassov, K.: Intuitionistic Fuzzy Logics. Springer, Cham (2017)CrossRefzbMATHGoogle Scholar
  7. 7.
    Çuvalcioĝlu, G.: Some properties of \(E_{\alpha ,\beta }\) operator. Adv. Stud. Contemp. Math. 14(2), 305–310 (2007)Google Scholar
  8. 8.
    Dencheva, K.: Extension of intuitionistic fuzzy modal operators Open image in new window and Open image in new window. In: Proceedings of the Second International IEEE Symposium: Intelligent Systems, Varna, 22–24 June 2004, vol. 3, pp. 21–22 (2004)Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Intelligent Systems LaboratoryProf. Asen Zlatarov UniversityBourgasBulgaria

Personalised recommendations