In this paper we extend the concept of an $L$-fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring $R$, and we show that each level left (resp. right) ideal of an $L$-fuzzy left (resp. right) ideal $\mu $ of $R$ is characteristic iff $\mu $ is $L$-fuzzy characteristic.
The fuzzification of (normal) $B$-subalgebras is considered, and some related properties are investigated. A characterization of a fuzzy $B$-algebra is given.
In this note we show that a subtraction algebra is equivalent to an implicative BCK-algebra, and a subtraction semigroup is a special case of a BCI-semigroup.