Skip to main content
SpringerLink
Log in

Intuitionistic \(L\)-fuzzy ideals of \(BG\)-algebras

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

In this paper, the concept of an intuitionistic \(L\)-fuzzy sets to ideals and closed ideals of \(BG\)-algebras are applied. The notion of intuitionistic \(L\)-fuzzy closed ideals of \(BG\)-algebras are introduced and some related properties are investigated. Also, the product of intuitionistic \(L\)-fuzzy \(BG\)-algebras are investigated.

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. Ahn, S.S., Lee, H.D.: Fuzzy subalgebras of \(BG\)-algebras. Commun. Korean Math. Soc. 19(2), 243–251 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  2. Atanassov, K.T.: Intuitionistic fuzzy sets, Rep. No. 1697/84. Central Technical Library, Bulgarian Academy Science, Sofia (1983)

  3. Atanassov, K.T.: Intuitionistic Fuzzy Sets: Theory and Applications, Studies in fuzziness and soft computing, vol. 35. Physica-Verlag, Heidelberg (1999)

    Google Scholar 

  4. Atanassov, K.T., Stoeva, S.: Intuitionistic \(L\)-fuzzy sets. Cybern. Syst. Res. 2, 539–540 (1984)

    Google Scholar 

  5. Chandramouleeswaran, M., Muralikrishana, P.: On intuittionistic \(L\)-fuzzy subalgebras of \(BG\)-algebras. Int. Math. Forum 5(20), 995–1000 (2010)

    MATH  MathSciNet  Google Scholar 

  6. Cho, J.R., Kim, H.S.: On \(B\)-algebras and quasigroups. Quasigroups Relat. Syst. 8, 1–6 (2001)

    MATH  MathSciNet  Google Scholar 

  7. Goguen, J.A.: \(L\)-fuzzy sets. J. Math. Anal. Appl. 18(1), 145–174 (1967)

    Article  MATH  MathSciNet  Google Scholar 

  8. Imai, Y., Iseki, K.: On axiom system of propositional calculi.XIV. Proc. Japan Acad. 42(1), 19–22 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  9. Iseki, K.: An algebra related with a propositional calculus. Proc. Japan Acad. 42(1), 26–29 (1966)

    Article  MATH  MathSciNet  Google Scholar 

  10. Iseki, K., Tanaka, S.: Ideal theory of \(BCK\)-algebras. Math. Japonica 21, 351–366 (1976)

    MATH  MathSciNet  Google Scholar 

  11. Kim, C.B., Kim, H.S.: On \(BG\)-algebras. Demonstr. Math. 41, 497–505 (2008)

    MATH  Google Scholar 

  12. Muthuraj, R., Sridharan, M., Sitharselvam, P.M.: Fuzzy \(BG\)-ideals in \(BG\)-algebra. Int. J. Comput. Appl. 2(1), 26–30 (2010)

    Google Scholar 

  13. Neggers, J., Kim, H.S.: On \(B\)-algebras. Math. Vensik 54, 21–29 (2002)

    MATH  MathSciNet  Google Scholar 

  14. Saeid, A.B.: Fuzzy topological \(BG\)-algbra. Int. Math. J. 6(2), 121–127 (2005)

    MATH  MathSciNet  Google Scholar 

  15. Senapati, T., Bhowmik, M., Pal, M.: Some results on intuittionistic \(L\)-fuzzy subalgebras of \(BG\)-algebras (communicated)

  16. Senapati, T., Bhowmik, M., Pal, M.: Fuzzy \(B\)-subalgebras of \(B\)-algebra with respect \(t\)-norm. J. Fuzzy Set Value Anal. 2012 (2012)

  17. Senapati, T., Bhowmik, M., Pal, M.: Interval-valued intuitionistic fuzzy \(BG\)-subalgebras. J. Fuzzy Math. 20(3), 707–720 (2012)

    MATH  MathSciNet  Google Scholar 

  18. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors would like to express sincere appreciation to the referees for their valuable suggestions and comments helpful in improving this paper.

Author information

Authors and Affiliations

  1. Department of Mathematics, V. T. T. College, Midnapore, 721 101, India

    Monoranjan Bhowmik

  2. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102, India

    Tapan Senapati & Madhumangal Pal

Authors
  1. Monoranjan Bhowmik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tapan Senapati
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Madhumangal Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Monoranjan Bhowmik.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bhowmik, M., Senapati, T. & Pal, M. Intuitionistic \(L\)-fuzzy ideals of \(BG\)-algebras. Afr. Mat. 25, 577–590 (2014). https://doi.org/10.1007/s13370-013-0139-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-013-0139-5

Keywords

Mathematics Subject Classification (2000)

Search

Navigation