  Fractal interpolation function (FIF) is a special type of continuous function
which interpolates certain data set and the attractor of the Iterated function
system (IFS) corresponding to the data set is the graph of the FIF. Coalescence
Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and
non self-affine in nature depending on the free variables and constrained free
variables for a generalized IFS. In this article graph directed iterated
function system for a finite number of generalized data sets is considered and
it is shown that the projections of the attractors on $\mathbb{R}^{2}$ is the
graph of the CHFIFs interpolating the corresponding data sets.
