Skip to main content

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

  • Conference paper
  • First Online:
Novel Developments in Uncertainty Representation and Processing

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Atanassov, K.: Intuitionistic fuzzy sets. Proceedings of VII ITKR’s Session, Sofia (Bulgarian) (1983)

    MATH  Google Scholar 

  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. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. Elsevier 20(1), 87–96 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  4. Atanassov, K.: Geometrical interpretations of the elements of the intuitionistic fuzzy objects. Preprint IM-MFAIS-1-89, Sofia (1989)

    Google Scholar 

  5. Atanassov, K.: Intuitionistic Fuzzy Sets. Springer, Heidelberg (1999)

    Book  MATH  Google Scholar 

  6. Atanassov, K.: On four intuitionistic fuzzy topological operators. Mathware Soft Comput. 8, 65–70 (2001)

    MathSciNet  MATH  Google Scholar 

  7. Atanassov, K.: On Intuitionistic Fuzzy Sets Theory. Springer, Berlin (2012)

    Book  MATH  Google Scholar 

  8. Atanassov, K.: Index Matrices: Towards an Augmented Matrix Calculus. Springer, Cham (2014)

    MATH  Google Scholar 

  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. 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. 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. 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. 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. InterCriteria Research Portal. http://www.intercriteria.net/publications

  15. Rangasamy, P., Vassilev, P., Atanassov, K.: New topological operators over intuitionistic fuzzy sets. Adv. Stud. Contemp. Math. 18(1), 49–57 (2009)

    MathSciNet  MATH  Google Scholar 

  16. World Economic Forum. The Global Competitiveness Report 2014–2015. http://www.weforum.org/issues/global-competitiveness

Download references

Acknowledgments

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

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Vassia Atanassova .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Atanassova, V., Vardeva, I., Sotirova, E., Doukovska, L. (2016). Traversing and Ranking of Elements of an Intuitionistic Fuzzy Set in the Intuitionistic Fuzzy Interpretation Triangle. In: Atanassov, K., et al. Novel Developments in Uncertainty Representation and Processing. Advances in Intelligent Systems and Computing, vol 401. Springer, Cham. https://doi.org/10.1007/978-3-319-26211-6_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-26211-6_14

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26210-9

  • Online ISBN: 978-3-319-26211-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics