  K-frames, a new generalization of frames, were recently considered by L.
Gavruta in connection with atomic systems and some problems arising in sampling
theory. Also, fusion frames are an important generalization of frames, applied
in a variety of applications. In the present paper, we introduce the notion of
K-fusion frames in Hilbert spaces and obtain several approaches for identifying
of $K$-fusion frames. The main purpose is to reconstruct the elements from the
range of the bounded operator $K$ on a Hilbert space H by using a family of
closed subspaces in H. This work will be useful in some problems in sampling
theory which are processed by fusion frames. For this end, we present some
descriptions for duality of K-fusion frames and also resolution of the operator
K to provide simple and concrete constructions of duals of K-fusion frames.
Finally, we survey the robustness of K-fusion frames under some perturbations.
