  The surface singular braid monoid corresponds to marked graph diagrams of
knotted surfaces in braid form. In a quest to resolve linearity problem for
this monoid, we will show that if it is defined on at least two or at least
three strands, then its two or respectively three dimensional representations
are not faithful. We will also derive new presentations for the surface
singular braid monoid, one with reduced the number of defining relations, and
the other with reduced the number of its singular generators. We include
surface singular braid formulations of all knotted surfaces in Yoshikawa's
table.
