  Strange correlators are useful tools for diagnosing symmetry-protected
topological states from their bulk wave functions. We study strange correlators
for one-dimensional fermionic symmetry-protected topological states using
fixed-point wave functions, and show that a combination of strange correlators
constructed using fermion annihilation operators and bosonic order parameters
can fully diagnose the classification from such wave functions. By converting
the strange correlator to a correlation in a one-dimensional statistical
problem described by transfer matrices, we show that when the wave function is
topologically nontrivial, the corresponding strange correlator exhibits a
long-range-order behavior, which can be analyzed from the symmetry properties
of the transfer matrices constructed from the fixed-point wave function. Our
general argument is demonstrated by several concrete examples.
