  In the context of non-Hermitian quantum mechanics, many systems are known to
possess a pseudo PT symmetry , i.e. the non-Hermitian Hamiltonian H is related
to its adjoint H^{{\dag}} via the relation, H^{{\dag}}=PTHPT . We propose a
derivation of pseudo PT symmetry and {\eta} -pseudo-Hermiticity simultaneously
for the time dependent non-Hermitian Hamiltonians by intoducing a new metric
{\eta}(t)=PT{\eta}(t) that not satisfy the time-dependent quasi-Hermiticity
relation but obeys the Heisenberg evolution equation. Here, we solve the
SU(1,1) time-dependent non-Hermitian Hamiltonian and we construct a
time-dependent solutions by employing this new metric and discuss a concrete
physical applications of our results.
