Skip to main content
Log in

T-fuzzy KU-ideals of KU-algebras

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

In this paper, using t-norm T, the notion of (imaginable) T-fuzzy KU-ideals of KU-algebras are introduced and investigated their related results. Images and preimages of KU-ideals under homomorphism are investigated. Using level subsets of KU-algebras, some characterization theorems are given. The Cartesian product and T-product of T-fuzzy KU-ideals of KU-algebras are discussed.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Akram, M., Yaqoob, N., Kavikumar, J.: Interval valued \((\tilde{\theta }, \tilde{\delta })\)-fuzzy \(KU\)-ideals of \(KU\)-algebras. Int. J. Pure Appl. Math. 92(3), 335–349 (2014)

    Article  MATH  Google Scholar 

  2. Akram, M., Yaqoob, N., Gulistan, M.: Cubic \(KU\)-subalgebras. Int. J. Pure Appl. Math. 89(5), 659–665 (2013)

    Google Scholar 

  3. Bhowmik, M., Senapati, T., Pal, M.: Intuitionistic \(L\)-fuzzy ideals of \(BG\)-algebras. Afr. Mat. 25(3), 577–590 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gulistan, M., Shahzad, M., Ahmed, S.: On \((\alpha,\beta )\)-fuzzy \(KU\)-ideals of \(KU\)-algebras. Afr. Mat. 26(3–4), 651–661 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hadzic, O., Pap, E.: Fixed Point Theory in Probabilistic Metric Spaces. Kluwer Academic Publishers, Dordrecht (2001)

    Book  MATH  Google Scholar 

  6. Hajek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)

    Book  MATH  Google Scholar 

  7. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)

    Book  MATH  Google Scholar 

  8. Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Position paper I: basic analytical and algebraic properties. Fuzzy Sets Syst. 143, 5–26 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Menger, K.: Statistical metrics. Proc. Nat. Acad. Sci. USA 8, 535–537 (1942)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mostafa, S.M., Abd-Elnaby, M.A., Yousef, M.M.: Fuzzy ideals of \(KU\)-algebras. Int. Math. Forum. 6(63), 3139–3149 (2011)

    MathSciNet  MATH  Google Scholar 

  11. Mostafa, S.M., Kareem, F.F.: \(N\)-fold commutative \(KU\)-Algebras. Int. J. Algebra. 8(6), 267–275 (2014)

    Article  MATH  Google Scholar 

  12. Muhiuddin, G.: Bipolar fuzzy \(KU\)-subalgebras\(\setminus \)ideals of \(KU\)-algebras. Ann. Fuzzy Math. Inform. 8(3), 409–418 (2014)

    MathSciNet  MATH  Google Scholar 

  13. Prabpyak, C., Leerawat, U.: On ideals and congruences in \(KU\)-algebras. Sci. Magna. 5(1), 54–57 (2009)

    MathSciNet  Google Scholar 

  14. Prabpyak, C., Leerawat, U.: On isimorphism of \(KU\)-algebras. Sci. Magna. 5(3), 25–31 (2009)

    MathSciNet  MATH  Google Scholar 

  15. Rosenfeld, A.: Fuzzy Groups. J. Math. Anal. Appl. 35, 512–517 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  16. Schweizer, B., Sklar, A.: Statistical metric spaces. Pac. J. Math. 10, 313–334 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  17. Senapati, T.: \(T\)-fuzzy \(KU\)-subalgebras of \(KU\)-algebras. Ann. Fuzzy Math. Inform. 10(2), 261–270 (2015)

    MathSciNet  MATH  Google Scholar 

  18. Senapati, T., Bhowmik, M., Pal, M., Davvaz, B.: Atanassov’s intuitionistic fuzzy translations of intuitionistic fuzzy subalgebras and ideals in \(BCK/BCI\)-algebras. Eurasian Math. J. 6(1), 96–114 (2015)

    MathSciNet  MATH  Google Scholar 

  19. Senapati, T., Jana, C., Bhowmik, M., Pal, M.: \(L\)-fuzzy \(G\)-subalgebras of \(G\)-algebras. J. Egypt. Math. Soc. 23, 219–223 (2015)

    Article  MATH  Google Scholar 

  20. Senapati, T., Kim, C.S., Bhowmik, M., Pal, M.: Cubic subalgebras and cubic closed ideals of \(B\)-algebras. Fuzzy Inf. Eng. 7(2), 129–149 (2015)

    Article  MathSciNet  Google Scholar 

  21. Senapati, T., Bhowmik, M., Pal, M.: Fuzzy dot structure of \(BG\)-algebras. Fuzzy Inf. Eng. 6(3), 315–329 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Senapati, T.: Bipolar Fuzzy structure of \(BG\)-subalgebras. J. Fuzzy Math. 23(1), 209–220 (2015)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  24. Yaqoob, N., Mostafa, S.M., Ansari, M.A.: On cubic \(KU\)-ideals of \(KU\)-algebras. ISRN Algebra, p. 10 (2013) (Article ID 935905). https://doi.org/10.1155/2013/935905

  25. Zadeh, L.A.: Fuzzy sets. Inform. Control. 8(3), 338–353 (1965)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Tapan Senapati.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Senapati, T. T-fuzzy KU-ideals of KU-algebras. Afr. Mat. 29, 591–600 (2018). https://doi.org/10.1007/s13370-018-0561-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-018-0561-9

Keywords

Mathematics Subject Classification

Navigation