East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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SOME RESULTS ON FUZZY IDEAL EXTENSIONS OF BCK-ALGEBRAS

  • Received : 2009.05.25
  • Accepted : 2010.03.12
  • Published : 2010.05.31
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Abstract

In this paper, we prove that the extension ideal of a fuzzy characteristic ideal of a positive implicative BCK-algebra is a fuzzy characteristic ideal. We introduce the notion of the extension of intuitionistic fuzzy ideal of BCK-algebras and some properties of fuzzy intuitionistic ideal extensions of BCK-algebra are investigated.

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References

  1. K. T. Atanassov, An intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
  2. K. Iseki, On ideals in BCK-algebras, Math. Seminar Notes (presently, Kobe J. Math.) 3 (1975), 1-12.
  3. K. Iseki and S. Tanaka, An introduction to theory of BCK-algebras, Math. Japon. 23 (1978), 1-26.
  4. W. K. Jeong, Fuzzy ideals extensions of BCK-algebras, Far East J. Math. Sci. 7 (2002), 67-75.
  5. Y. B. Jun, S. M. Hong, J. Meng and X. L. Xin, Characterizations of fuzzy positive implicative ideals in BCK-algebras, Math. Japon. 40 (1994), 503-507.
  6. Y. B. Jun, S. M. Hong and R. E. Roh, Fuzzy characteristic subalgebras/ideals of a BCK-algebra, Pusan Kyongnam Math. J. 9 (1993), 127-132.
  7. Y. B. Jun and K. H. Kim, Intuitionistic fuzzy ideals of BCK-algebras, Internat. J. Math & Math. Sci. 24 (2000), 839-849. https://doi.org/10.1155/S0161171200004610
  8. Y. B. Jun E. H. Roh, J. Meng and X. L. Xin, Fuzzy prime and fuzzy irreducible ideals in BCK-algebras, Soochow J. Math. 21 (1995), 49-56.
  9. J. Meng and Y. B. Jun, BCK-algebras, Kyungmoonsa, Seoul, Korea 1994.
  10. T. Sakuragi, On fuzzy quasi-ideals and their radicals in a commutative BCK-algebra, Math. Japon. 46 (1997), 485-490.
  11. T. Sakuragi, On prime fuzzy quasi-ideals and primary fuzzy quasi-ideals, in a commu- tative BCK-algebra, Math. Japon. 48 (1997), 437-445.
  12. O. G. Xi, Fuzzy BCK-algebras, Math. Japon. 36 (1991), 935-942.
  13. X. Y. Xie, Fuzzy ideals extensions of semigroups, Soochow J. Math. 27 (2001), 125-138.
  14. L. A. Zadeh, Fuzzy sets, Inform and Control. 8 (1965), 378-353.