Fuzzy Information and Engineering

, Volume 4, Issue 2, pp 181–193 | Cite as

Fuzzy ideals of ternary semigroups

Original Article


In this paper, we introduce fuzzy ideals of ternary semigroups and study their related properties. Here we define fuzzy left (right, lateral) ideals of ternary semigroups and characterize regular and intra-regular ternary semigroups by using the concept of fuzzy ideals of ternary semigroups.


Fuzzy ternary subsemigroup Fuzzy left (right, lateral) ideal Regular ternary semigroup Intra-regular ternary semigroup 


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  1. 1.
    Dutta T K, Kar S and Maity B K (2008) On ideals in regular ternary semigroups. Discussiones Mathematicae. General Algebra and Applications 28: 147–159MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Kuroki N (1981) On fuzzy ideals and fuzzy bi-ideals in semigroups. Fuzzy Sets and Systems 5: 203–215MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Kuroki N (1991) On fuzzy semigroups. Information Sciences 3: 203–236MathSciNetCrossRefGoogle Scholar
  4. 4.
    Lehmer D H (1932) A ternary analogue of abelian groups. American Journal of Mathematics 54: 329–338MathSciNetCrossRefGoogle Scholar
  5. 5.
    Los J (1955) On the extending of models I. Fundamenta Mathematicae 42: 38–54MathSciNetMATHGoogle Scholar
  6. 6.
    Mordeson J N, Malik D S and Kuroki N (2003) Fuzzy semigroups. SpringerGoogle Scholar
  7. 7.
    Pu PM, Lui YM (1980) Fuzzy topology I. Neighborhood structure of a fuzzy point and Moore-Smith convergence. Journal of Mathematical Analysis and Applications 76: 571–599MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Rosenfeld A (1971) Fuzzy groups. Journal of Mathematical Analysis and Applications 35: 512–517MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Santiago M L and Bala S S (2010) Ternary semigroups. Semigroup Forum 81: 380–388MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Sioson F M (1965) Ideal theory in ternary semigroups. Mathematica Japonica 10: 63–84MathSciNetMATHGoogle Scholar
  11. 11.
    Wang X P, Mo ZW and Liu WJ (1992) Fuzzy ideals generated by fuzzy point in semigroups. Sichuan Shifan Daxue Xuebao Ziran Kexue Ban 15: 17–24MathSciNetGoogle Scholar
  12. 12.
    Zadeh L A (1965) Fuzzy sets. Information and Control 8: 338–353MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Fuzzy Information and Engineering Branch of the Operations Research Society of China 2012

Authors and Affiliations

  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia

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