  In theory of topological classification, the 2D topological superconductors
without time reversal symmetry are characterized by Chern numbers. However, in
reality, we find the Chern numbers can not reveal the whole properties of the
boundary states of the topological superconductors. We figure out some
particle-hole symmetry related $\mathbf{Z}_{2}$ invariants, which provide more
additional information of the topological superconductors than the Chern
numbers provide. With the $\mathbf{Z}_{2}$ invariant, we define weak and strong
topological superconductors in 2D systems. Moreover, we explain the causes of
mismatch between the Chern numbers and the numbers of boundary states in
topological superconductors, and claim that the robust Majorana zero modes are
characterized by the $\mathbf{Z}_{2}$ invariant rather than the Chern numbers.
We also extend the $\mathbf{Z}_{2}$ invariants to 3D non-time-reversal symmetry
superconductor systems including gapful and gapless situations.
