  We present a new type of matrix regularization, which is based on
matrix-valued functions defined on a cylinder. If non-commutative coordinates
of a fuzzy space are defined by a regularization of such functions, we show
that a classical limit for the fuzzy spaces exists, when the matrix-valued
functions nearly commute. In this case, the classical limit of the fuzzy space
is a manifold, which is composed of coordinate patches that are defined by the
diagonal entries of the diagonalized matrix-valued functions. As applications,
an interpolation for direct sums of fuzzy spaces is described and a fuzzy
string vertex with classical limit, i.e. a surface interconnecting three
circles, is constructed.
