Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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FUZZY SUB-IMPLICATIVE IDEALS OF BCI-ALGEBRAS

  • Jun, Young-Bae (Department of Mathematics Education, Gyeongsang National University)
  • Published : 2002.05.01
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Abstract

We Consider the fuzzification of sub-implicative ideals in BCI-algebras, and investigate some related properties. We give conditions for a fuzzy ideal to be a fuzzy sub-implicative ideal. we show that (1) every fuzzy sub-implicative ideal is a fuzzy ideal, but the converse is not true, (2) every fuzzy sub-implicative ideal is a fuzzy positive implicative ideal, but the converse is not true, and (3) every fuzzy p-ideal is a fuzzy sub-implicative ideal, but the converse is not true. Using a family of sub-implicative ideals of a BCI-algebra, we establish a fuzzy sub-implicative ideal, and using a level set of a fuzzy set in a BCI-algebra, we give a characterization of a fuzzy sub-implicative ideal.

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References

  1. Y. B. Jun and J. Meng, Fuzzy p-ideals in Bel-algebras, Math. Japon. 40 (1994),no. 2, 271-282.
  2. Y. L. Liu and J. Meng, Sub-implicative ideals and sub-commutative ideals of BCl-algebras, Soochow J. Math. (to appear).
  3. Y. L. Liu and J. Meng, Fuzzy ideals in BCl-algebras, Fuzzy Sets and Systems 123 (2001), 227-237. https://doi.org/10.1016/S0165-0114(00)00047-6
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