Afrika Matematika

, Volume 29, Issue 3–4, pp 641–654 | Cite as

Homomorphism and isomorphism of soft int-groups

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Abstract

In this paper, soft int-groups, soft normal int-groups and their basic properties are presented. Normal soft int-subgroup of a soft int-group is defined and relations concerning them are given. Then, homomorphism and isomorphism theorems are applied to the soft int-groups.

Keywords

Soft set Soft product Soft int-group Normal soft int-group Soft coset 

Mathematics Subject Classification

03G25 20N25 08A72 06D72 

References

  1. 1.
    Abou-Zaid, S.: On fuzzy subgroups. Fuzzy Sets Syst. 55, 237–240 (1993)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Akgül, M.: Some properties of fuzzy groups. J. Math. Anal. Appl. 133, 93–100 (1988)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Aktaş, H., Çağman, N.: Soft sets and soft groups. Inform. Sci. 177, 2726–2735 (2007)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Ali, M.I., Feng, F., Liu, X., Min, W.K., Shabir, M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547–1553 (2009)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Anthony, J.M., Sherwood, H.: Fuzzy subgroups redefined. J. Math. Anal. Appl. 69, 124–130 (1979)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Asaad, M.: Groups and fuzzy subgroups. Fuzzy Sets Syst. 39, 323–328 (1991)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Bhattacharya, P., Mujherjee, N.P.: Fuzzy groups, some group theoretic analogs, Part II. Inform. Sci. 41, 77–91 (1987)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bhutani, K.R.: Fuzzy sets, fuzzy relations and fuzzy groups: Some interrelations. Inform. Sci. 73, 107–115 (1993)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Çağman, N., Enginoğlu, S.: Soft set theory and uni-int decision making. Eur. J. Oper. Res. 207, 848–855 (2010)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Çağman, N., Çıtak, F., Aktaş, H.: Soft int-group and its applications to group theory. Neural Comput. Appl. 21(Suppl 1), 151 (2012).  https://doi.org/10.1007/s00521-011-0752-x
  11. 11.
    Çağman, N., Karataş, S., Enginoğlu, S.: Soft Topology. Comput. Math. Appl. 62, 351–358 (2011)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Çağman, N., Karataş, S.: Intuitionistic fuzzy soft set theory and its decision making. Intell. Fuzzy Syst. 24(4), 829–836 (2013)MathSciNetMATHGoogle Scholar
  13. 13.
    Das, P.S.: Fuzzy groups and level subgroups. J. Math. Anal. Appl. 84, 264–269 (1981)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Dixit, V.N., Kumar, R., Ajamal, N.: Level subgroups and union of fuzzy subgroups. Fuzzy Sets Syst. 37, 359–371 (1990)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Feng, F., Li, Y., Çağman, N.: Generalized uni-int decision making schemes based on choice value soft sets. Eur. J. Oper. Res. 220, 162–170 (2012)MathSciNetCrossRefMATHGoogle Scholar
  16. 16.
    Karaaslan, F., Çağman, N., Enginoğlu, S.: Soft lattices. J. New Res. Sci. 1, 5–17 (2012)Google Scholar
  17. 17.
    Kaygısız, K.: On soft int-Groups. Ann. Fuzzy Math. Inform. 4(2), 365–375 (2012)MathSciNetMATHGoogle Scholar
  18. 18.
    Kaygısız, K.: Normal soft int-groups. arXiv:1209.3157
  19. 19.
    Kim, J.G.: Fuzzy orders relative to Fuzzy subgroups. Inform. Sci. 80, 341–348 (1994)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Maji, P.K., Biswas, R., Roy, A.R.: Soft set theory. Comput. Math. Appl. 45, 555–562 (2003)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Molodtsov, D.A.: Soft set theory-first results. Comput. Math. Appl. 37, 19–31 (1999)MathSciNetCrossRefMATHGoogle Scholar
  22. 22.
    Mordeson, J.N., Bhutani, K.R., Rosenfeld, A.: Fuzzy group theory. Springer, Berlin (2005)CrossRefMATHGoogle Scholar
  23. 23.
    Mujherjee, N.P., Bhattacharya, P.: Fuzzy groups, some group theoretic analogs. Inform. Sci. 39, 247–268 (1986)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Rosenfeld, A.: Fuzzy groups. J. Math. Anal. Appl. 35, 512–517 (1971)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Sezgin, A., Atagün, A.O.: On operations of soft sets. Comput. Math. Appl. 61(5), 1457–1467 (2011)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Sezgin, A., Atagün, A.O., Çağman, N.: Soft intersection near-rings with its applications. Neural Comput. Appl. 21, 221–229 (2012)CrossRefGoogle Scholar
  27. 27.
    Zadeh, L.A.: Fuzzy sets. Inform. Control 8, 338–353 (1965)CrossRefMATHGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.TokatTurkey

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