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http://dx.doi.org/10.4134/BKMS.2002.39.2.185

FUZZY SUB-IMPLICATIVE IDEALS OF BCI-ALGEBRAS  

Jun, Young-Bae (Department of Mathematics Education, Gyeongsang National University)
Publication Information
Bulletin of the Korean Mathematical Society / v.39, no.2, 2002 , pp. 185-198 More about this Journal
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;
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