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FUZZY SUB-IMPLICATIVE IDEALS OF BCI-ALGEBRAS

Jun, Young-Bae

  • Published : 2002.05.01

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.

Keywords

(fuzzy) sub-implicative ideal;fuzzy positive implicative ideal;fuzzy p-ideal;(fuzzy) characteristic sub-implicative ideal

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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Cited by

  1. Algorithms and computations for foldedness of P-ideals in BCI-algebras vol.6, pp.4, 2008, https://doi.org/10.1016/j.jal.2008.04.001
  2. Doubt Atanassov's intuitionistic fuzzy Sub-implicative ideals inBCI-algebras vol.8, pp.2, 2015, https://doi.org/10.1080/18756891.2015.1001948
  3. Computational methods for study of foldness of H-ideals in BCI-algebras vol.12, pp.4, 2007, https://doi.org/10.1007/s00500-007-0176-9