DOI QR코드

DOI QR Code

FUZZY TRANSLATIONS AND FUZZY MULTIPLICATIONS OF HYPER BCK-ALGEBRAS

Kang, Min-Su

  • Received : 2011.07.13
  • Accepted : 2011.08.01
  • Published : 2011.09.25

Abstract

Fuzzy ${\alpha}$-translations, (normalized, maximal) fuzzy extensions and fuzzy multiplications of fuzzy hyper BCK-subalgebras in hyper BCK-algebras are discussed. Relations among fuzzy ${\alpha}$ translations, (normalized, maximal) fuzzy extensions and fuzzy multiplications are investigated.

Keywords

fuzzy ${\alpha}$-translation;fuzzy hyper BCK-subalgebra;fuzzy extension;fuzzy S-extension;fuzzy ${\gamma}$-multiplication

References

  1. D. Dubois and H. Prade, Fuzzy sets and systems: Theory and Applications, Academic Press, 1980.
  2. H. Harizavi, Prime weak hyper BCK-ideals of lower hyper BCK-semilattice, Sci. Math. Jpn. 68 (2008), no. 3, 353-360.
  3. Y. B. Jun and W. H. Shim, Fuzzy implicative hyper BCK-ideals of hyper BCK-algebras, Internat. J. Math. Math. Sci. 29 (2002), no. 2, 63-70. https://doi.org/10.1155/S016117120201195X
  4. Y. B. Jun and X. L. Xin, Scalar elements and hyperatoms of hyper BCK-algebras, Scientiae Mathematicae 2 (1999), no. 3, 303-309.
  5. Y. B. Jun and X. L. Xin, Fuzzy hyper BCK-ideals of hyper BCK-algebras, Sci. Math. Jpn. 53 (2) (2001), 353-360.
  6. Y. B. Jun, X. L. Xin, E. H. Roh and M. M. Zahedi, Strong hyper BCK-ideals of hyper BCK-algebras, Math. Japonica 51 (3) (2000), 493-498.
  7. Y. B. Jun, M. M. Zahedi, X. L. Xin and R. A. Borzooei, On hyper BCK-algebras, Italian J. of Pure and Appl. Math. 8 (2000), 127-136.
  8. F. Marty, Sur une generalization de la notion de groupe, 8th Congress Math. Scandinaves, Stockholm (1934), 45-49.
  9. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
  10. H. -J. Zimmermann, Fuzzy Set Theory and its Applications, Kluwer-Nijhoff Publishing, 1985.