On Some Modal Type Intuitionistic Fuzzy Operators

  • Krassimir T. Atanassov
  • Janusz Kacprzyk
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)CrossRefzbMATHGoogle Scholar
  3. 3.
    Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)CrossRefzbMATHGoogle 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)CrossRefzbMATHGoogle Scholar
  7. 7.
    Blackburn, P., van Bentham, J., Wolter, F.: Handbook of Modal Logic. Elsevier, Amsterdam (2007)zbMATHGoogle Scholar
  8. 8.
    Carnap, R.: Meaning and Necessity. University of Chicago Press, Chicago (1947)zbMATHGoogle Scholar
  9. 9.
    Carnielli, W., Pizzi, C.: Modalities and Multimodalities. Springer, Heidelberg (2008)CrossRefzbMATHGoogle Scholar
  10. 10.
    Chagrov, A., Zakharyaschev, M.: Modal Logic. Oxford University Press, Oxford (1997)zbMATHGoogle Scholar
  11. 11.
    Feys, R.: Modal Logics. Gauthier, Paris (1965)zbMATHGoogle 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)zbMATHGoogle Scholar
  14. 14.
    Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefMathSciNetzbMATHGoogle 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