Convergence on Intuitionistic Fuzzy Metric Space

  • M. El Hassnaoui
  • Said MellianiEmail author
  • L. S. Chadli
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 372)


Using the idea of intuitionistic fuzzy metric space, due to George and Veeramani [fuzzy sets and systems 90(1997) 365–368], and the results of metric space by Jin Han Park [intuitionistic fuzzy metric spaces (2004) 1036–1046] we define a hausdroff topology on a fuzzy metric space. Also we prove an equivalence between the convergence in a fuzzy separable metric space and the adhesion of intuitionistic fuzzy set.


  1. 1.
    K. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets Syst. 2, 87–96 (1989)zbMATHGoogle Scholar
  2. 2.
    D. Coker, An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst. 88, 81–89 (1997)MathSciNetCrossRefGoogle Scholar
  3. 3.
    M.A. Erceg, Metric spaces in fuzzy set theory. J. Math. Anal. Appl. 69, 316–328 (1979)MathSciNetCrossRefGoogle Scholar
  4. 4.
    J.H. Park, Intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 22(5), 1039–1046 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    A. George, P. Veeramani, On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64(3), 395–399 (1994)MathSciNetCrossRefGoogle Scholar
  6. 6.
    E.P. Klement, Operations on fuzzy sets: an axiomatic approach. Inform. Sci. 27, 221–232 (1984)MathSciNetCrossRefGoogle Scholar
  7. 7.
    O. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces. Kybernetica 11, 326–334 (1975)MathSciNetzbMATHGoogle Scholar
  8. 8.
    R. Owen, Fuzzy Set Theory (Kluwer Academic Publishers, 1996)Google Scholar
  9. 9.
    K. Menger, Statistical metrics. Proc. Nat. Acad. Sci. 28, 535–537 (1942)MathSciNetCrossRefGoogle Scholar
  10. 10.
    J.R. Munkres, Topologya First Course (Prentice-Hall, 1975)Google Scholar
  11. 11.
    J. Nagata, Modern General Topology (North-Holland, 1974)Google Scholar
  12. 12.
    B. Schweizer, A. Sklar, Statistical metric spaces. Pac. J. Math. 10, 314–334 (1960)MathSciNetzbMATHGoogle Scholar
  13. 13.
    R.R. Yager, On a general class of fuzzy connectives. Fuzzy Sets Syst. 4, 235–242 (1980)MathSciNetCrossRefGoogle Scholar
  14. 14.
    L.A. Zadeh, Fuzzy sets. Inform. Control 8, 338–353 (1965)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • M. El Hassnaoui
    • 1
  • Said Melliani
    • 1
    Email author
  • L. S. Chadli
    • 1
  1. 1.Sultan Moulay Slimane UniversityBeni MellalMorocco

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