Traversing and Ranking of Elements of an Intuitionistic Fuzzy Set in the Intuitionistic Fuzzy Interpretation Triangle

  • Vassia AtanassovaEmail author
  • Ivelina Vardeva
  • Evdokia Sotirova
  • Lyubka Doukovska
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 401)


In this leg of research, we explore the question of traversing and ranking elements of an intuitionistic fuzzy set in the intuitionistic fuzzy interpretation triangle. This is necessary in the light of the new developments of the InterCriteria Analysis (ICA), a decision support approach based on intuitionistic fuzzy sets and index matrices. In the ICA, from the data about the evaluations or measurements of a set of objects against a set of criteria, we perform pairwise comparisons of any two objects against each pair of criteria, and perform computations that yield in result intuitionistic fuzzy pairs of numbers in the [0; 1]-interval that give the levels of correlation between any two of the evaluation criteria. In previous works, the correlations between the criteria (hence the term ‘intercriteria’) were analysed separately, by first setting priority on either the membership, or the non-membership component, and plotting them linearly; while currently the efforts are oriented to handling both IF components simultaneously by plotting them in the plane of the intuitionistic fuzzy interpretation triangle.


Intercriteria analysis Intuitionistic fuzzy sets Triangular geometrical interpretation of intuitionistic fuzzy sets Closure Interior 



The authors are grateful for the support provided by the National Science Fund of Bulgaria under grant DFNI-I-02-5/2014.


  1. 1.
    Atanassov, K.: Intuitionistic fuzzy sets. Proceedings of VII ITKR’s Session, Sofia (Bulgarian) (1983)zbMATHGoogle Scholar
  2. 2.
    Atanassov, K.: Modal and topological operators, defined over intuitionistic fuzzy sets. In: Youth scientific contributions, vol. 1, pp. 18–21. Academic Publishing House, Sofia (1985)Google Scholar
  3. 3.
    Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. Elsevier 20(1), 87–96 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Atanassov, K.: Geometrical interpretations of the elements of the intuitionistic fuzzy objects. Preprint IM-MFAIS-1-89, Sofia (1989)Google Scholar
  5. 5.
    Atanassov, K.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999)CrossRefzbMATHGoogle Scholar
  6. 6.
    Atanassov, K.: On four intuitionistic fuzzy topological operators. Mathware Soft Comput. 8, 65–70 (2001)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)CrossRefzbMATHGoogle Scholar
  8. 8.
    Atanassov, K.: Index Matrices: Towards an Augmented Matrix Calculus. Springer, Cham (2014)zbMATHGoogle Scholar
  9. 9.
    Atanassov, K., Mavrov, D., Atanassova, V.: InterCriteria decision making. A new approach for multicriteria decision making, based on index matrices and intuitionistic fuzzy sets. Issues Intuitionistic Fuzzy Sets Generalized Nets 11, 1–8 (2014)Google Scholar
  10. 10.
    Atanassova, V.: Interpretation in the intuitionistic fuzzy triangle of the results, obtained by the intercriteria analysis. In: Proceedings of IFSA-EUSFLAT 2015, 30.06.2015–03.07.2015, pp. 1369–1374. Atlantic Press, Gijon, Spain (2015)Google Scholar
  11. 11.
    Atanassova, V., Doukovska, L., Atanassov, K., Mavrov, D.: InterCriteria decision making approach to EU member states competitiveness analysis. In: Proceedings of 4th International Symposium on Business Modeling and Software Design, pp. 289–294. 24–26 Jun 2014, Luxembourg (2014)Google Scholar
  12. 12.
    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
  13. 13.
    Atanassova, V., Vardeva, I.: Sum- and average-based approach to criteria shortlisting in the InterCriteria analysis. Int. J. Notes Intuitionistic Fuzzy Sets 20(4):41–46 (2014)Google Scholar
  14. 14.
    InterCriteria Research Portal.
  15. 15.
    Rangasamy, P., Vassilev, P., Atanassov, K.: New topological operators over intuitionistic fuzzy sets. Adv. Stud. Contemp. Math. 18(1), 49–57 (2009)MathSciNetzbMATHGoogle Scholar
  16. 16.
    World Economic Forum. The Global Competitiveness Report 2014–2015.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Vassia Atanassova
    • 1
    Email author
  • Ivelina Vardeva
    • 2
  • Evdokia Sotirova
    • 2
  • Lyubka Doukovska
    • 3
  1. 1.Bioinformatics and Mathematical Modelling DepartmentIBPhBME – Bulgarian Academy of SciencesSofiaBulgaria
  2. 2.Intelligent Systems Laboratory“Prof. Dr. Asen Zlatarov” UniversityBurgasBulgaria
  3. 3.Intelligent Systems DepartmentIICT – Bulgarian Academy of SciencesSofiaBulgaria

Personalised recommendations