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

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Novel Developments in Uncertainty Representation and Processing

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 401))

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.

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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

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Acknowledgments

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

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Authors and Affiliations

  1. Bioinformatics and Mathematical Modelling Department, IBPhBME – Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, 1113, Sofia, Bulgaria

    Vassia Atanassova

  2. Intelligent Systems Laboratory, “Prof. Dr. Asen Zlatarov” University, 1 “Prof. Yakimov” Blvd, 8010, Burgas, Bulgaria

    Ivelina Vardeva & Evdokia Sotirova

  3. Intelligent Systems Department, IICT – Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 2, 1113, Sofia, Bulgaria

    Lyubka Doukovska

Authors
  1. Vassia Atanassova
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  2. Ivelina Vardeva
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  3. Evdokia Sotirova
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  4. Lyubka Doukovska
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Corresponding author

Correspondence to Vassia Atanassova .

Editor information

Editors and Affiliations

  1. Inst. of Biophy. & Biomedical Eng., Bulgarian Academy of Sciences, Sofia, Bulgaria

    Krassimir T. Atanassov

  2. Division of Graduate Studies, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Oscar Castillo

  3. Sys Res Intit of Polish Acad of Science, Intelligent Systems Laboratory, Warsaw, Poland

    Janusz Kacprzyk

  4. Warsaw School of Information Technology, Polish Academy of Sciences, Warsaw, Poland

    Maciej Krawczak

  5. Div of Gdu Stud,CalzTecn sn,Fra.TomAqu, Tijuana Institute of Technology, Tijuana, Baja California, Mexico

    Patricia Melin

  6. Intelligent Systems Laboratory, Asen Zlatarov University, Bourgas, Bulgaria

    Sotir Sotirov

  7. Intelligent Systems Laboratory, “Prof. Dr. Asen Zlatarov” University, Burgas, Bulgaria

    Evdokia Sotirova

  8. Systems Research Institute, Polish Academy of Sciences, Warszawa, Poland

    Eulalia Szmidt

  9. Dept. of Tele. & Info. Processing, Ghent University, Gent, Belgium

    Guy De Tré

  10. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Sławomir Zadrożny

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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

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

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26210-9

  • Online ISBN: 978-3-319-26211-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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