  Vassiliev introduced filtered invariants of knots using an unknotting
operation, called crossing changes. Goussarov, Polyak, and Viro introduced
other filtered invariants of virtual knots, which order is called GPV-order,
using an unknotting operation, called virtualization. We defined other filtered
invariants, which order is called $F$-order, of virtual knots using an
unknotting operation, called forbidden moves. In this paper, we show that the
set of virtual knot invariants of $F$-order $\le n+1$ is strictly stronger than
that of $F$-order $\le n$ and that of GPV-order $\le 2n+1$. To obtain the
result, we show that the set of virtual knot invariants of $F$-order $\le n$
contains every Goussarov-Polyak-Viro invariant of GPV-order $\le 2n+1$, which
implies that the set of virtual knot invariants of $F$-order is a complete
invariant of classical and virtual knots.
