DOI QR코드

DOI QR Code

BIPOLAR-VALUED FUZZY IDEAL EXTENSIONS OF BCK-ALGEBRAS

  • Received : 2012.11.11
  • Accepted : 2013.01.11
  • Published : 2013.02.15

Abstract

The notions of the extensions of bipolar fuzzy ideals, bipolar fuzzy prime ideals and bipolar fuzzy commutative ideals in BCK-algebras are introduced, and several properties are investigated.

Keywords

References

  1. Y. Imai and K. Iseki, On axiom systems of propositional calculi XIV, Proc. Japan Academy 42 (1966), 19-22.
  2. K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Math. Japon. 23 (1978), 1-26.
  3. W. K. Jeong, Fuzzy ideal extensions of BCK-algebras, Far East J. Math. Sci. 7(1) (2002), 67-75.
  4. Y. B. Jun, Fuzzy topological BCK-algebras, Math. Japon. 38 (1993), 1059-1063.
  5. K. J. Lee, Bipolar fuzzy subalgebras and bipolar fuzzy ideals of BCK/BCI-algebras, Bull. Malays. Math. Sci. Soc. 32 (2009), 361-373.
  6. K. M. Lee, Bipolar-valued fuzzy sets and their operations, Proc. Int. Conf. on Intelligent Technologies, Bangkok, Thailand (2000), 307-312.
  7. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoonsa , Seoul, Korea, 1994.
  8. O. G. Xi, Fuzzy BCK-algebras, Math. Japon. 36 (1991), 935-942.
  9. X. Y. Xie, Fuzzy ideals extensions of semigroups, Soochow J. Math. 27 (2001), 125-138.
  10. L. A. Zadeh, Fuzzy sets, Inform and Control. 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X