  In this paper, we define the concept of soft $g$-frame in soft Hilbert spaces
by extending the concept of soft from frame to $g$-frame. We then show some
properties of the soft $g$-frames in soft Hilbert spaces.
  Among other results, we show that the $g$-frame operator is associated with a
soft, finite, self-adjoining, reversible, and finite inverse $g$-frame and get
the dual g-frames. In addition, we prove that every element in Hilbert's soft
space satisfies the theorem of $g$-frame decomposition.
