We introduce the notion of $M$-BCK/BCI-algebras 

and $M$-fuzzy subalgebras for a set $M$, and investigate some

of their properties. We establish $M$-fuzzy subalgebras from

old one. We give characrerizations of $M$-fuzzy subalgebras.

We show that the $M$-homomorphic image and inverse image of

an $M$-fuzzy subalgebra is also an $M$-fuzzy subalgebra.