  We show that the fermionic matrix model can be realized by
$W$-representation. We construct the Virasoro constraints with higher algebraic
structures, where the constraint operators obey the Witt algebra and null
3-algebra. The remarkable feature is that the character expansion of the
partition function can be easily derived from such Virasoro constraints. It is
a $\tau$-function of the KP hierarchy. We construct the fermionic Aristotelian
tensor model and give its $W$-representation. Moreover, we analyze the
fermionic red tensor model and present the $W$-representation and character
expansion of the partition function.
