Skip to main content
SpringerLink
Log in

(∈, ∈ ∨ q)-fuzzy subnear-rings and ideals

  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

Our aim in this paper is to introduce and study the new sort of fuzzy subnear-ring (ideal and prime ideal) of a near-ring called (∈, ∈ ∨q)-fuzzy subnear-ring (ideal and prime ideal). These fuzzy subnear-rings (ideals) are characterized by their level ideals. Finally, we give a generalization of (∈, ∈ ∨q)-fuzzy subnear-rings (ideals).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abou-Zaid S (1991) On fuzzy subnear-rings and ideals. Fuzzy Sets Syst 44:139–146

    Google Scholar 

  2. Bhakat SK (2000) (∈ , ∈ ∨ q)-fuzzy normal, quasinormal and maximal subgroups. Fuzzy Sets Syst 112:299–312

    Google Scholar 

  3. Bhakat SK (1999) (∈ ∨ q)-level subsets. Fuzzy Sets Syst 103:529–533

    Google Scholar 

  4. Bhakat SK, Das P (1992) On the definition of a fuzzy subgroup. Fuzzy Sets Syst 51:235–241

    Google Scholar 

  5. Bhakat SK, Das P (1996) (∈ , ∈ ∨ q)-fuzzy subgroup. Fuzzy Sets Syst 80:359–368

    Google Scholar 

  6. Bhakat SK, Das P (1996) Fuzzy subrings and ideals redifind. Fuzzy Sets Syst 81:383–393

    Google Scholar 

  7. Clay JR (1992) Near-Rings: geneses and applications. Oxford, New York

  8. Das PS (1981) Fuzzy groups and level subgroups. J Math Anal Appl 85:264–269

    Google Scholar 

  9. Davvaz B (2003) A study on the structure of Hv-near-rings modules. Indian J Pure Appl Math 34(5):693–700

    Google Scholar 

  10. Davvaz B (2000) Hv-near-rings. Math Japonica 52(3):387–392

    Google Scholar 

  11. Davvaz B (2001) Fuzzy ideals of near-rings with interval-valued membership functions. J Sci I R Iran 12(2):171–175

    Google Scholar 

  12. Davvaz B (1999) On hypernear-rings and fuzzy hyperideals. J Fuzzy Math 7(3):745–753

    Google Scholar 

  13. Dutta TK, Biswas BK (2002) On fuzzy congruence of a near-ring module. Fuzzy Sets Syst 112:343–348

    Google Scholar 

  14. Jun YB, Kim KH (2002) Interval-valued fuzzy R-subgroups of near-rings. Indian J Pure Appl Math 33(1):71–80

    Google Scholar 

  15. Jun YB, Kim KH (2001) Intuitionistic fuzzy R-subgroups of near-rings. Soochow J Math 27(3):243–253

    Google Scholar 

  16. Jun YB, Kim KH, Yon HY (1999) Intuitionistic fuzzy ideals of near-rings. J Inst Math Comput Sci Math Ser 12(3):221–228

    Google Scholar 

  17. Kim KH (2002) T-fuzzy R-subgroups of near-rings. Panam Math J 12(2):21–29

    Google Scholar 

  18. Kim KH, Jun YB (2002) A note on fuzzy R-subgroups of near-rings. Soochow J Math 28(4):339–346

    Google Scholar 

  19. Kim KH, Jun YB (2000) On fuzzy R-subgroups of near-rings. J Fuzzy Math 8(3):549–558

    Google Scholar 

  20. Kim KH, Jun YB (1999) Anti fuzzy R-subgroups of near-rings. Sci Math 2(2):147–153

    Google Scholar 

  21. Kim KH, Jun YB (2001) Normal fuzzy R-subgroups in near-rings. Fuzzy Sets Syst 121:341–345

    Google Scholar 

  22. Kim KH, Jun YB (1996) On fuzzy ideals of near-rings. Bull Korean Math Soc 33(4):593–601

    Google Scholar 

  23. Kim KH, Jun YB (2001) Abnormalization of anti fuzzy ideals in near-rings. Far East J Math Sci (FJMS) 3(1):15–25

    Google Scholar 

  24. Liu WJ (1982) Fuzzy invariant subgroups and fuzzy ideals. Fuzzy Sets Syst 8:133–139

    Google Scholar 

  25. Mordeson JN, Malik MS (1998) Fuzzy Commutative Algebra. World Publishing

  26. Meldrum JDP (1985) Near-rings and their links with groups. Pitman, New York

  27. Narayanan Al (2002) Fuzzy ideals on strongly regular near-rings. J Indean Math Soc (N.S.) 69(1–4):193–199

    Google Scholar 

  28. Pilz G (1977) Near-rings. The theory and its applications. North-Holand, Amsterdam

  29. Rosenfeld A (1971) Fuzzy groups. J Math Anal Appl 35:512–517

    Google Scholar 

  30. Saikia HK, Barthakur LK (2003) On fuzzy N-subgroups and fuzzy ideals of near-rings and near-ring groups. J Fuzzy Math 11(3):567–580

    Google Scholar 

  31. Vasantha Kandasamy WB (1997) On fuzzy complex near-rings. J Math Educ 31(2):90–91

    Google Scholar 

  32. Xuehai Yuan, Cheng Zhang, Yonghong Ren, (2003) Generalized fuzzy groups and many-valued implications. Fuzzy Sets Syst 138:205–211

  33. Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Yazd University, 89195-741, Yazd, Iran

    B. Davvaz

Authors
  1. B. Davvaz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. Davvaz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Davvaz, B. (∈, ∈ ∨ q)-fuzzy subnear-rings and ideals. Soft Comput 10, 206–211 (2006). https://doi.org/10.1007/s00500-005-0472-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-005-0472-1

Keywords

Mathematics Subject Classification (2000)

Search

Navigation