Skip to main content
SpringerLink
Log in

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

  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper, we introduce the notions of (∈, ∈∨q)-fuzzy subnear-ring, (∈, ∈∨q)-fuzzy ideal and (∈, ∈∨q)-fuzzy quasi-ideal of near-rings and find more generalized concepts than those introduced by others. The characterization of such (∈, ∈ ∨q)-fuzzy ideals are also obtained.

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. S.K. Bhakat and P. Das, (∈, ∈ ∨q)-fuzzy subgroup, Fuzzy sets and systems,80 (1996), 359–393.

    Article  MATH  MathSciNet  Google Scholar 

  2. S.K. Bhakat and P. Das,Fuzzy subrings and ideals redefined, Fuzzy sets and systems,81 (1996), 383–393.

    Article  MATH  MathSciNet  Google Scholar 

  3. S.K. Bhakat and P. Das,On the definition of a fuzzy subgroup, Fuzzy sets and systems,51 (1992), 235–241.

    Article  MATH  MathSciNet  Google Scholar 

  4. S.K. Bhakat and P. Das,q-similitudes and q-fuzzy partitions, Fuzzy sets and systems,51 (1992), 195–202.

    Article  MATH  MathSciNet  Google Scholar 

  5. V.N. Dixit, R. Kumar and N. Ajmal,On fuzzy rings, Fuzzy sets and systems,49 (1992), 205–213.

    Article  MATH  MathSciNet  Google Scholar 

  6. Günter Pilz,Near-rings: The theory and its applications North-Holland Publishing Company, Amsterdam, 1983.

    MATH  Google Scholar 

  7. R. Kumar,Certain fuzzy ideals of rings redefined, Fuzzy sets and systems,46 (1992), 251–260.

    Article  MATH  MathSciNet  Google Scholar 

  8. R. Kumar,Fuzzy irreducible ideals in rings, Fuzzy sets and systems,42 (1991), 369–379.

    Article  MATH  MathSciNet  Google Scholar 

  9. W. Liu,Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and systems,8 (1982), 133–139.

    Article  MATH  MathSciNet  Google Scholar 

  10. P.P. Ming and L.Y. Ming,Fuzzy Topology I: Neighbourhood structure of a fuzzy point and moore-smith convergence, J. Math. Anal. Appl.,76 (1980), 571–599.

    Article  MATH  MathSciNet  Google Scholar 

  11. AL. Narayanan,Contributions to the algebraic structures in fuzzy theory, Ph.D. Thesis, Annamalai University, 2001.

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

    Article  MATH  MathSciNet  Google Scholar 

  13. Salah Abon-Zaid,On fuzzy subnear-rings and ideals, Fuzzy sets and systems,44 (1991), 139–146.

    Article  MathSciNet  Google Scholar 

  14. L.A. Zadeh,Fuzzy sets, Information and Control,8 (1965), 338–353.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Annamalai University, 608002, Annamalainagar, Tamilnadu, India

    AL. Narayanan & T. Manikantan

Authors
  1. AL. Narayanan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Manikantan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to AL. Narayanan.

Additional information

AL. Narayanan, M.Sc., M.Phil., Ph.D., is a Reader in Mathematics at Annamalai University, Annamalainagar, Tamilnadu, India. He has published research papers in reputed national and international journals, including journal of Indian mathematical society and the journal of fuzzy mathematics. His research interests center on the theory of fuzzy algebra and fuzzy topology.

T. Manikantan received his M.Sc. and M.Phil. from Annamalai University in the year 1999 and 2000 respectively. He is doing Ph.D. at Annamalai University under the direction of AL. Narayanan. He has published research papers in the journal of fuzzy mathematics. His research interests focus on the theory of fuzzy algebra.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Narayanan, A., Manikantan, T. (∈, ∈∨q)-fuzzy subnear-rings and (∈, ∈∨q)-fuzzy ideals of near-rings. JAMC 18, 419–430 (2005). https://doi.org/10.1007/BF02936584

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02936584

AMS Mathematics Subject Classification

Key words and phrases

Search

Navigation