On Some Modal Type Intuitionistic Fuzzy Operators

Part of the Studies in Computational Intelligence book series (SCI, volume 623)


A review of two groups of basic modal type operators, defined over the intuitionistic fuzzy sets, is given. Two new modal operators are introduced for the first time, and some of their properties are discussed. Some open problems are formulated.


Intuitionistic fuzzy operator Intuitionistic fuzzy set Modal logic 

AMS Classification



  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.)Google Scholar
  2. 2.
    Atanassov, K.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  3. 3.
    Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)CrossRefMATHGoogle Scholar
  4. 4.
    Atanassov, K.: A short remark on operator X a,b,c,d,e,f. Notes Intuitionistic Fuzzy Sets 19(1) (in press) (2013)Google Scholar
  5. 5.
    Atanassov, K., Gargov, G.: Intuitionistic fuzzy logic operators of a set theoretical type. In: Lakov, D. (eds.) Proceedings of the First Workshop on Fuzzy Based Expert Systems, Sofia, Sept. 28–30, pp. 39–42 (1994)Google Scholar
  6. 6.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)CrossRefMATHGoogle Scholar
  7. 7.
    Blackburn, P., van Bentham, J., Wolter, F.: Handbook of Modal Logic. Elsevier, Amsterdam (2007)MATHGoogle Scholar
  8. 8.
    Carnap, R.: Meaning and Necessity. University of Chicago Press, Chicago (1947)MATHGoogle Scholar
  9. 9.
    Carnielli, W., Pizzi, C.: Modalities and Multimodalities. Springer, Heidelberg (2008)CrossRefMATHGoogle Scholar
  10. 10.
    Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford University Press, Oxford (1997)MATHGoogle Scholar
  11. 11.
    Feys, R.: Modal Logics. Gauthier, Paris (1965)MATHGoogle Scholar
  12. 12.
    Goldblatt, R.: Mathematics of Modality. In: CSLI Lecture Notes No. 43. University of Chicago Press, Chicago (1993)Google Scholar
  13. 13.
    Zeman, J.: Modal Logic, The Lewis-Modal Systems. Oxford University Press, Oxford (1973)MATHGoogle Scholar
  14. 14.
    Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Systems Research Institute – Polish Academy of SciencesWarsawPoland

Personalised recommendations