⊤-Fuzzy Subgroups with Thresholds

  • Bao Qing Hu
  • Yan Qing Niu
Part of the Advances in Soft Computing book series (AINSC, volume 54)


This paper mainly studies the ⊤-fuzzy subgroups with thresholds. Product concepts of fuzzy sets are generalized to t-norm and properties of ⊤-fuzzy subgroups with thresholds are discussed.


Fuzzy Subgroups ⊤-Fuzzy Subgroups Products of fuzzy Sets ⊤-fuzzy subgroup with thresholds 


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  1. 1.
    Zadeh, L.A.: Fuzzy sets. Inform. And Control 8, 338–353 (1965)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Rosenfeld, A.: Fuzzy groups. J. Math. Anal Appl. 35, 512–517 (1971)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Das, P.S.: Fuzzy groups and level subgroups. J. Math. Anal. Appl. 84, 264–269 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Mukherjee, N.P., Bhattacharya, P.: Fuzzy normal subgroups and fuzzy cosets. Inform. Sci. 34, 225–239 (1984)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Sidky, F.I., Mishref, M.A.: Fuzzy cosets and cyclic and abelian fuzzy subgroup. Fuzzy Sets and Systems 43, 243–250 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Akgul, M.: Some properties of fuzzy groups. J. Math. Anal. Appl. 133, 93–100 (1988)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Anthony, J.M., Sherwood, H.: Fuzzy groups refined. J. Math. Anal. Appl. 69, 124–130 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Anthony, J.M., Sherwwood, H.: A characterization of fuzzy groups. Fuzzy Sets and System 7, 297–305 (1982)zbMATHCrossRefGoogle Scholar
  9. 9.
    Bhakat, S.K., Das, P.: On the definition of a fuzzy subgroup. Fuzzy Sets and Systems 51, 235–241 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Bhakat, S.K., Das, P.: ( ∈ , ∈ ∨ q)-fuzzy subgroup. Fuzzy Sets and Systems 80, 359–368 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Yuan, X., Zhang, C., Ren, Y.: Generalized fuzzy groups and many-valued implications. Fuzzy Sets and Systems 138, 205–211 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. North-Holland, Amsterdam (1983)zbMATHGoogle Scholar
  13. 13.
    Ajmal, N.: Fuzzy group theory: A comparison of different notions of product of fuzzy sets. Fuzzy Sets and Systems 110, 437–446 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Liu, W.-J.: Fuzzy invariant subgroups and fuzzy ideals. Fuzzy Sets and System 21, 133–139 (1982)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Bao Qing Hu
    • 1
  • Yan Qing Niu
    • 1
  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina

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