We define the notion of an interval-valued fuzzy

subalgebra/$\circ$-subalgebra/ideal (briefly, an i-v fuzzy

subalgebra/$\circ$-subalgebra/ideal) of a BCK-algebra.  We

study how the homomorphic images and inverse images of i-v

fuzzy subalgebras become i-v fuzzy subalgebras. We give

relations between i-v fuzzy subalgebras/$\circ$-subalgebras

and i-v fuzzy ideals. We give a condition for an i-v fuzzy set

in a BCK-algebra with condition $(S)$ to be an i-v fuzzy

ideal. We also state characterizations of an i-v fuzzy

subalgebra/ideal.