Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

HYPER K-SUBALGEBRAS BASED ON FUZZY POINTS

  • Received : 2010.03.10
  • Published : 2011.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

Generalizations of the notion of fuzzy hyper K-subalgebras are considered. The concept of fuzzy hyper K-subalgebras of type (${\alpha},{\beta}$) where ${\alpha}$, ${\beta}$ ${\in}$ {${\in}$, q, ${\in}{\vee}q$, ${\in}{\wedge}q$} and ${\alpha}{\neq}{\in}{\wedge}q$. Relations between each types are investigated, and many related properties are discussed. In particular, the notion of (${\in}$, ${\in}{\vee}q$)-fuzzy hyper K-subalgebras is dealt with, and characterizations of (${\in}$, ${\in}{\vee}q$)-fuzzy hyper K-subalgebras are established. Conditions for an (${\in}$, ${\in}{\vee}q$)-fuzzy hyper K-subalgebra to be an (${\in}$, ${\in}$)-fuzzy hyper K-subalgebra are provided. An (${\in}$, ${\in}{\vee}q$)-fuzzy hyper K-subalgebra by using a collection of hyper K-subalgebras is established. Finally the implication-based fuzzy hyper K-subalgebras are discussed.

Keywords

References

  1. S. K. Bhakat and P. Das, On the definition of a fuzzy subgroup, Fuzzy Sets and Systems 51 (1992), no. 2, 235-241. https://doi.org/10.1016/0165-0114(92)90196-B
  2. S. K. Bhakat and P. Das, (${\in}, {\in} {\vee}q$)-fuzzy subgroup, Fuzzy Sets and Systems 80 (1996), no. 3, 359-368. https://doi.org/10.1016/0165-0114(95)00157-3
  3. A. Borumand Saeid, R. A. Borzoei, and M. M. Zahedi, (Weak) implicative hyper K-ideals, Bull. Korean Math. Soc. 40 (2003), no. 1, 123-137. https://doi.org/10.4134/BKMS.2003.40.1.123
  4. R. A. Borzooei, Hyper BCK and K-algebras, Ph. D. thesis, Shahid Bahonar University of Kerman, 2000.
  5. R. A. Borzooei, A. Hasankhani, M. M. Zahedi, and Y. B. Jun, On hyper K-algebras, Math. Japon. 52 (2000), no. 1, 113-121.
  6. Y. B. Jun, On fuzzy hyper K-subalgebras of hyper K-algebras, Sci. Math. 3 (2000), no. 1, 67-75
  7. Y. B. Jun, On (${\alpha}, {\beta}$)-fuzzy subalgebras of BCK/BCI-algebras, Bull. Korean Math. Soc. 42 (2005), no. 4, 703-711. https://doi.org/10.4134/BKMS.2005.42.4.703
  8. Y. B. Jun, Fuzzy subalgebras of type (${\alpha}, {\beta}$) in BCK/BCI-algebras, Kyungpook Math. J. 47 (2007), no. 3, 403-410.
  9. Y. B. Jun and W. H. Shim, Fuzzy positive implicative hyper K-ideals in hyper K- algebras, Honam Math. J. 25 (2003), no. 1, 43-52.
  10. Y. B. Jun and W. H. Shim, Fuzzy hyper K-ideals of hyper K-algebras, J. Fuzzy Math. 12 (2004), no. 4, 861-871.
  11. Y. B. Jun and S. Z. Song, Generalized fuzzy interior ideals in semigroups, Inform. Sci. 176 (2006), no. 20, 3079-3093. https://doi.org/10.1016/j.ins.2005.09.002
  12. Y. B. Jun, M. M. Zahedi, X. L. Xin, and R. A. Borzoei, On hyper BCK-algebras, Ital. J. Pure Appl. Math. No. 8 (2000), 127-136.
  13. F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45-49.
  14. V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158 (2004), 277-288. https://doi.org/10.1016/j.ins.2003.07.008
  15. P. M. Pu and Y. M. Liu, Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980), no. 2, 571-599. https://doi.org/10.1016/0022-247X(80)90048-7
  16. M. S. Ying, A new approach for fuzzy topology. I, Fuzzy Sets and Systems 39 (1991), no. 3, 303-321. https://doi.org/10.1016/0165-0114(91)90100-5
  17. M. S. Ying, On standard models of fuzzy modal logics, Fuzzy Sets and Systems 26 (1988), no. 3, 357-363. https://doi.org/10.1016/0165-0114(88)90128-5