  In this paper, we introduce the concept of $K$-fusion frames and propose the
duality for such frames. The relation between the local frames of $K$-fusion
frames with their dual is studied. The elements from the range of a bounded
linear operator $K$ can be reconstructed by $K$-frames. Also, we establish
$K$-fusion frame multipliers and investigate reconstruction of the range of $K$
by them.
