Traversing and Ranking of Elements of an Intuitionistic Fuzzy Set in the Intuitionistic Fuzzy Interpretation Triangle
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.
KeywordsIntercriteria 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.
- 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
- 4.Atanassov, K.: Geometrical interpretations of the elements of the intuitionistic fuzzy objects. Preprint IM-MFAIS-1-89, Sofia (1989)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
- 16.World Economic Forum. The Global Competitiveness Report 2014–2015. http://www.weforum.org/issues/global-competitiveness