Neural Computing and Applications

, Volume 21, Issue 2, pp 391–397 | Cite as

Fuzzy isomorphism theorems of soft rings

  • Xianping Liu
  • Dajing Xiang
  • Jianming Zhan
Original Article


The concepts of fuzzy ideals of soft rings are introduced. The first, second and third fuzzy isomorphism theorems of soft rings are established respectively. In particular, some classes of quotient rings are characterized by their fuzzy ideals.


Soft rings Fuzzy ideals Quotient rings Fuzzy isomorphism theorems 



The authors are extremely grateful to the referees for giving them many valuable comments and helpful suggestions, which help to improve the presentation of this paper. This research was supported by National Natural Science Foundation of China (60875034), the Natural Science Foundation of Education Committee of Hubei Province, China (D20092901), and the Natural Science Foundation of Hubei Province, China (2009CDB340).


  1. 1.
    Aktas H, Cağman N (2007) Soft sets and soft groups. Inform Sci 177:2726–2735MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Chen D, Tsang ECC, Yeung DS, Wang X (2005) The parametrization reduction of soft sets and its applications. Comput Math Appl 49:757–763MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Fang JX (1994) Fuzzy homomorphism and fuzzy isomorphism. Fuzzy Sets Syst 63:237–242zbMATHCrossRefGoogle Scholar
  4. 4.
    Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56:2621–2628MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Jun YB (2008) Soft BCK/BCI-algebras. Comput Math Appl 56:1408–1413MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Jun YB, Park CH (2008) Applications of soft sets in ideal theory of BCK/BCI-algebras. Inform Sci 178:2466–2475MathSciNetzbMATHGoogle Scholar
  7. 7.
    Liu W (1982) Fuzzy invariant subgroups and fuzzy ideals. Fuzzy Sets Syst 8:133–139zbMATHCrossRefGoogle Scholar
  8. 8.
    Liu X, Xiang D, Zhan J, Shum KP, Isomorphism theorems for soft rings. Algebra Colloquium (in press)Google Scholar
  9. 9.
    Liu Y, Liu S (2004) Fuzzy isomorphism theorems of groups. Far East J Appl Math 16:77–89MathSciNetzbMATHGoogle Scholar
  10. 10.
    Liu YL, Meng J, Xin XL (2001) Quotient rings induced via fuzzy ideals. Korean J Comput Appl Math 8:631–643MathSciNetzbMATHGoogle Scholar
  11. 11.
    Ma X, Zhan J (2009) Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings. Inform Sci 179:1249–1268MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44:1077–1083MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Maji PK, Roy AR, Biswas R (2003) Soft set theory. Comput Math Appl 45:555–562MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Molodtsov D (1999) Soft set theory-first results. Comput Math Appl 37:19–31MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Mukherjee TK, Sen MK (1987) On fuzzy ideals on a ring I. Fuzzy Sets Syst 21:99–104MathSciNetzbMATHCrossRefGoogle Scholar
  16. 16.
    Rosenfeld A (1971) Fuzzy groups. J Math Anal Appl 35:512–517MathSciNetzbMATHCrossRefGoogle Scholar
  17. 17.
    Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353MathSciNetzbMATHCrossRefGoogle Scholar
  18. 18.
    Zhan J, Dudek WA (2007) Fuzzy h-ideal of hemirings. Inform Sci 177:876–886MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  1. 1.Department of MathematicsHubei Institute for NationalitiesEnshiChina

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