  Classification and construction of symmetry protected topological (SPT)
phases in interacting boson and fermion systems have become a fascinating
theoretical direction in recent years. It has been shown that the (generalized)
group cohomology theory or cobordism theory can give rise to a complete
classification of SPT phases in interacting boson/spin systems. Nevertheless,
the construction and classification of SPT phases in interacting fermion
systems are much more complicated, especially in 3D. In this work, we revisit
this problem based on the equivalent class of fermionic symmetric local unitary
(FSLU) transformations. We construct very general fixed point SPT wavefunctions
for interacting fermion systems. We naturally reproduce the partial
classifications given by special group super-cohomology theory, and we show
that with an additional $\tilde{B}H^2(G_b, \mathbb Z_2)$ (the so-called
obstruction free subgroup of $H^2(G_b, \mathbb Z_2)$) structure, a complete
classification of SPT phases for three-dimensional interacting fermion systems
with a total symmetry group $G_f=G_b\times \mathbb Z_2^f$ can be obtained for
unitary symmetry group $G_b$. We also discuss the procedure of deriving a
general group super-cohomology theory in arbitrary dimensions.
