On Separability of Intuitionistic Fuzzy Sets

  • Evgeniy MarinovEmail author
  • Peter Vassilev
  • Krassimir Atanassov
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 401)


Intuitionistic fuzzy sets prove very useful in modelling uncertain and imprecise information when in the evaluations, concerned with a bipolar type of evidence, the “pro” and “contra” estimations do not sum to one (truth) but there is a degree of uncertainty. Relying on the concept of IF-neighbourhoods, introduced in Marinov et al. (On intuitionistic fuzzy metric neighbourhoods, 2015), we propose in this paper a few notions of separability between intuitionistic fuzzy sets and give some applications employing the extended modal operators.


Distances Intuitionistic fuzzy sets Operators Separability 



The authors are grateful for the support provided by Grant DFNI-I-02-5 “InterCriteria Analysis—A New Approach to Decision Making” of the Bulgarian National Science Fund.


  1. 1.
    Adams, C., Franzosa, R.: Introduction to Topology—Pure and Applied. Pearson Prentice Hall, USA (2008)Google Scholar
  2. 2.
    Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  3. 3.
    Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)CrossRefzbMATHGoogle Scholar
  4. 4.
    Atanassov, K., Mavrov, D., Atanassova, V.: Intercriteria decision making: a new approach for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets. In: Issues in Intuitionistic Fuzzy Sets and Generalized Nets, vol. 11, pp. 1–8 (2014)Google Scholar
  5. 5.
    Atanassova, V., Mavrov, D., Doukovska, L., Atanassov, K.: Discussion on the threshold values in the interCriteria decision making approach. Int. J. Notes Intuitionistic Fuzzy Sets 20(2), 94–99 (2014)Google Scholar
  6. 6.
    Atanassov, K., Vassilev, P., Tcvetkov, R.: Intuitionistic Fuzzy Sets, Measures and Integrals. “Prof. M. Drinov” Academic Publishing House, Sofia (2013)Google Scholar
  7. 7.
    Ban, A.: Intuitionistic Fuzzy Measures. Theory and Applications. Nova Science Publishers, New York (2006)zbMATHGoogle Scholar
  8. 8.
    Deng-Feng, L.: Multiattribute decision making models and methods using intuitionistic fuzzy sets. J. Comput. Syst. Sci. 70, 73–85 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Kuratowski, K.: Topology, vol. 1. Academic Press, New York (1966)Google Scholar
  10. 10.
    Marinov, E., Szmidt, E., Kacprzyk, J., Tcvetkov, R.: A modified weighted Hausdorff distance between intuitionistic fuzzy sets. IEEE Int. Conf. Intell. Syst. IS’12. 138–141 (2012)Google Scholar
  11. 11.
    Marinov, E., Vassilev, P., Atanassov, K.: On intuitionistic fuzzy metric neighbourhoods, IFSA-EUSFLAT 2015 (submitted)Google Scholar
  12. 12.
    Munkres, J.: Topology, 2nd edn. Prentice Hall (2000)Google Scholar
  13. 13.
    Narukawa, Y., Torra, V.: Non-monotonic fuzzy measure and intuitionistic fuzzy set. LNAI 3885, 150–160 (2006)Google Scholar
  14. 14.
    Szmidt, E.: Distances and similarities in intuitionistic fuzzy sets. In: Studies in Fuzziness and Soft Computing, vol. 307. Springer (2014)Google Scholar
  15. 15.
    Szmidt, E., Baldwin, J.: New similarity measure for intuitionistic fuzzy set theory and mass assignment theory. Notes Intuitionistic Fuzzy Sets 9(3), 60–76 (2003)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Szmidt, E., Baldwin, J.: Entropy for intuitionistic fuzzy set theory and mass assignment theory. Notes Intuitionistic Fuzzy Sets 10(3), 15–28 (2004)Google Scholar
  17. 17.
    Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114(3), 505–518 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Zadeh, L.: Fuzzy sets. Inf. Control 8, 338–353 (1965)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Evgeniy Marinov
    • 1
    Email author
  • Peter Vassilev
    • 1
  • Krassimir Atanassov
    • 1
  1. 1.Department of Bioinformatics and Mathematical ModellingInstitute of Biophysics and Biomedical Engineering, Bulgarian Academy of SciencesSofiaBulgaria

Personalised recommendations