Advertisement

Afrika Matematika

, Volume 29, Issue 1–2, pp 249–262 | Cite as

On interval valued intuitionistic fuzzy \(\beta \)-subalgebras

Article
  • 46 Downloads

Abstract

This paper deals the notion of interval valued instuitionistic fuzzy subalgebras of \(\beta \)-algebra and investigate some of the related results.

Keywords

\(\beta \)-algebra \(\beta \)-subalgebras Interval valued intuitionistic fuzzy sets Interval valued intuitionistic fuzzy \(\beta \)-subalgebra 

Mathematics subject classification

08A72 03E72 

Notes

Acknowledgements

The authors are highly grateful to the referees for their valuable comments, which improved the quality of this paper.

References

  1. 1.
    Ansari, M.A.A., Chandramouleeswaran, M.: Fuzzy \(\beta \)-subalgebras of \(\beta \)-algebras. Int. J. Math. Sci. Eng. Appl. 5(7), 239–249 (2013)Google Scholar
  2. 2.
    Atanassov, K.T.: Intuitionistic fuzzy sets, fuzzy sets and systems. J. Math. Appl. 20(1), 87–96 (1986)MATHGoogle Scholar
  3. 3.
    Attanassov, K.T., Gargov, G.: Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31(1), 343–349 (1989)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Biswas, R.: Rosenfeld’s fuzzy subgroups with interval valued membership functions. Fuzzy Sets Syst. 63(1), 87–90 (1994)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Hemavathi, P., Muralikrishna, P., Palanivel, K.: A note on interval valued fuzzy \(\beta \)-subalgebras. Global J. Pure Appl. Math. 11(4), 2553–2560 (2015)Google Scholar
  6. 6.
    Imai, Y., Iseki, K.: On axiom systems of propositional calculi. Proc. Jpn. Acad. 42(1), 19–22 (1973)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Iseki, K., Tanaka, S.: An introduction to theory of BCK-algebras. Math Jpn. 23, 1–26 (1973)MathSciNetMATHGoogle Scholar
  8. 8.
    Neggers, J., Kim, H.S.: On \(\beta \)-algebras. Math. Slovaca 52(5), 517–530 (2002)MathSciNetMATHGoogle Scholar
  9. 9.
    Neggers, J., Kim, H.S.: On \(\beta \)-algebras Mate. Vensik 54, 21–29 (2002)Google Scholar
  10. 10.
    Houng, S.M., Jun, Y.B., Kim, S.J., Kim, G.: Fuzzy BCI-subalgebras with interval valued membership functions. Math. Jpn. 40(2), 199–202 (1993)Google Scholar
  11. 11.
    Sujatha, K., Chandramouleeswaran, M., Muralikrishna, P.: On intuitionstic fuzzy \(\beta \)-subalgebras of \(\beta \)-algebras. Global J. Pure Appl. Math. 9(6), 559–566 (2013)Google Scholar
  12. 12.
    Senapati, T., Bhowmik, M., Pal, M.: Interval valued intuitionstic fuzzy BG-subalgebras. Math. Los Angel. 20(3), 707–720 (2012)MATHGoogle Scholar
  13. 13.
    Jun, Y.B., Kim, : \(\beta \)-subalgebras and related topics, commun. Korean Math. Soc. 27(2), 243–255 (2012)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Jun, Y.B.: Interval valued fuzzy sub algebras/ideas in BCK-algebras. Sci. Math. 3, 435–444 (2000)MathSciNetMATHGoogle Scholar
  15. 15.
    Zadeh, L.A.: Fuzzy sets. Inform. Control 8(3), 338–353 (1965)CrossRefMATHGoogle Scholar
  16. 16.
    Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. I. Inf. Sci. 8, 199–249 (1975)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Mathematics, School of Advanced SciencesVIT UniversityVelloreIndia
  2. 2.PG and Research Department of MathematicsMuthurangam Government Arts College (Autonomus)VelloreIndia

Personalised recommendations