  In the present paper, we describe new approaches for constructing virtual
knot invariants. The main background of this paper comes from formulating and
bringing together the ideas of biquandle (Kauffman and Radford) the virtual
quandle (Manturov), the ideas of quaternion biquandles by Roger Fenn and Andrew
Bartholomew, the concepts and properties of long virtual knots (Manturov), and
other ideas in the interface between classical and virtual knot theory. In the
present paper we present a new algebraic construction of virtual knot
invariants, give various presentations of it, and study several examples.
Several conjectures and unsolved problems are presented throughout the paper.
