The Intuitionistic Anti-fuzzy Subgroup in Group G

  • De-yuan Li
  • Cheng-yi Zhang
  • Sheng-quan Ma
Conference paper
Part of the Advances in Soft Computing book series (AINSC, volume 54)


On the basis of the intuitionistic fuzzy sets introduced by K.Atanassov, we first give definition to intuitionistic anti-fuzzy subgroups over group G and intuitionistic anti-fuzzy normal subgroups, which are different from the definitions in [1][3]and [5]. This paper proves a necessary and sufficient condition of intuitionistic anti-fuzzy subgroups and conditions of equivalence of intuitionistic anti-fuzzy normal subgroups. Some properties of theirs and quotient groups of intuitionistic anti-fuzzy normal subgroups are also discussed.


Intuitionistic fuzzy sets Intuitionistic anti-fuzzy subgroups Intuitionistic anti-fuzzy normal subgroups 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rosenfeld, A.: Fuzzy subgroups. J. Math. Anal. Appl. 35, 512–517 (1971)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Atanassov, K.: Intuituinistic fuzzy sets. Fuzzy Sets and Systems 20(1), 87–96 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Xiao-ping, L., Gui-ju, W.: Intuitionistic Fuzzy Group and Its Homomorphisic Image. Fuzzy Systems and Mathematic 14(1), 45–50 (2000)Google Scholar
  4. 4.
    Biswas, R.: Fuzzy subgroups and anti-fuzzy subgroups. Fuzzy Sets and Systems 35, 121–124 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bingxue, Y.: Intuitionistic fuzzy normal subgroup and intuitionistic fuzzy quotient group. Mathematical Theory And Applications 21(2), 73–77 (2001)MathSciNetGoogle Scholar
  6. 6.
    Zhengwei, S.: The Anti-fuzzy subgroup of group. Journal of Liaoning Normal University(Natural Science) 18(2), 99–101 (1995)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • De-yuan Li
    • 1
  • Cheng-yi Zhang
    • 1
  • Sheng-quan Ma
    • 1
  1. 1.Department of MathematicsHainan Normal UniversityHainanP.R. China

Personalised recommendations