New Modified Level Operator Nγ Over Intuitionistic Fuzzy Sets

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10333)

Abstract

The present paper takes the idea of the level operator N α,β and proposes a modification called N γ . The aim of the original level operator is to generate a subset of an intuitionistic fuzzy set A, called (αβ)-set, whose degrees of membership are above a given level (threshold) α and degrees of non-membership are below a given level β, where both α, β are fixed numbers in the [0, 1] interval and α + β ≤ 1. In the modification proposed here, we introduce the operator N γ that also generates a subset of an intuitionistic fuzzy set A, where the elements of the subset are those elements of A, for which the ratio of their degrees of membership to their degrees of non-membership, respectively, is greater or equal to a given number γ > 0.

Keywords

Intuitionistic fuzzy sets Level operator InterCriteria analysis 

Notes

Acknowledgements

The author is grateful for the support provided under Grant Ref. No. DFNI-I-02-5/2014 “Intercriteria Analysis: A New Method for Decision Making” funded by the National Science Fund of Bulgaria.

References

  1. 1.
    Angelova, N., Atanassov, K., Riecan, B.: Intercriteria analysis of the intuitionistic fuzzy implication properties. Notes on Intuitionistic Fuzzy Sets 21(5), 20–23 (2015)Google Scholar
  2. 2.
    Angelova, M., Roeva, O., Pencheva, T.: Intercriteria analysis of crossover and mutation rates relations in simple genetic algorithm. Ann. Comput. Sci. Inf. Syst. 5, 419–424 (2015)CrossRefGoogle Scholar
  3. 3.
    Atanassov, K.T.: Intuitionistic Fuzzy Sets, VII ITKR Session, Sofia, 20–23 June 1983 (1983). (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation 20(S1), S1–S6 (2016)Google Scholar
  4. 4.
    Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Atanassov, K.T.: Intuitionistic Fuzzy Sets. Springer Physica-Verlag, Heidelberg (1999)Google Scholar
  6. 6.
    Atanassov, K.: On Intuitionistic Fuzzy Sets. Springer, Berlin (2012)CrossRefMATHGoogle Scholar
  7. 7.
    Atanassov, K., Atanassova, V., Gluhchev, G.: Intercriteria analysis: ideas and problems. Notes on Intuitionistic Fuzzy Sets 21(1), 81–88 (2015)Google Scholar
  8. 8.
    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 in Intuitionistic Fuzzy Sets and Generalized Nets 11, 1–8 (2014)Google Scholar
  9. 9.
    Atanassova, V., Doukovska, L., Michalikova, A., Radeva, I.: Intercriteria analysis: from pairs to triples. Notes on Intuitionistic Fuzzy Sets 22(5), 98–110 (2016)Google Scholar
  10. 10.
    Doukovska, L., Atanassova, V., Sotirova, E., Vardeva, I., Radeva, I.: Defining Consonance Thresholds in InterCriteria Analysis: Overview (submitted)Google Scholar
  11. 11.
    Gottman, J.: Why marriages succeed or fail: and how you can make yours last. Simon and Schuster (1995)Google Scholar
  12. 12.
    Pencheva, T., Angelova, M., Vassilev, P., Roeva, O.: Intercriteria analysis approach to parameter identification of a fermentation process model. In: Atanassov, K.T., Castillo, O., Kacprzyk, J., Krawczak, M., Melin, P., Sotirov, S., Sotirova, E., Szmidt, E., Tré, G.D., Zadrożny, S. (eds.) Novel Developments in Uncertainty Representation and Processing. AISC, vol. 401, pp. 385–397. Springer, Cham (2016). doi: 10.1007/978-3-319-26211-6_33 CrossRefGoogle Scholar
  13. 13.
    Roeva, O., Vassilev, P.: Intercriteria analysis of generation gap influence on genetic algorithms performance. In: Atanassov, K.T., Castillo, O., Kacprzyk, J., Krawczak, M., Melin, P., Sotirov, S., Sotirova, E., Szmidt, E., Tré, G.D., Zadrożny, S. (eds.) Novel Developments in Uncertainty Representation and Processing. AISC, vol. 401, pp. 301–313. Springer, Cham (2016). doi: 10.1007/978-3-319-26211-6_26 CrossRefGoogle Scholar
  14. 14.
    Todorova, L., Vassilev, P., Surchev, J.: Using phi coefficient to interpret results obtained by intercriteria analysis. In: Atanassov, K.T., Castillo, O., Kacprzyk, J., Krawczak, M., Melin, P., Sotirov, S., Sotirova, E., Szmidt, E., Tré, G.D., Zadrożny, S. (eds.) Novel Developments in Uncertainty Representation and Processing. AISC, vol. 401, pp. 231–239. Springer, Cham (2016). doi: 10.1007/978-3-319-26211-6_20 CrossRefGoogle Scholar
  15. 15.
    Vassilev, P., Todorova, L., Andonov, V.: An auxiliary technique for intercriteria analysis via a three dimensional index matrix. Notes on Intuitionistic Fuzzy Sets 21(2), 71–76 (2015)Google Scholar
  16. 16.
    Project publications, Intercriteria.net. http://intercriteria.net/publications/

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Bioinformatics and Mathematical Modelling Department, Institute of Biophysics and Biomedical EngineeringBulgarian Academy of SciencesSofiaBulgaria

Personalised recommendations