  Motivated by the analogous properties of the $Z_c(3900/3885)$ and
$Z_{cs}(3985/4000)$, we tentatively assign the $Z_c(4020/4025)$ as the
$A\bar{A}$-type hidden-charm tetraquark state with the $J^{PC}=1^{+-}$, where
the $A$ denotes the axialvector diquark states, and explore the $A\bar{A}$-type
tetraquark states without strange, with strange and with hidden-strange via the
QCD sum rules in a consistent way. Then we explore the hadronic coupling
constants in the two-body strong decays of the tetraquark states without
strange and with strange via the QCD sum rules based on rigorous quark-hadron
duality, and acquire the partial decay widths and total decay widths. The
present calculations support assigning the $Z_c(4020/4025)$ as the
$A\bar{A}$-type tetraquark state with the $J^{PC}=1^{+-}$, while the
predictions for its strange cousin $Z_{cs}$ state can be confronted to the
experimental data in the future.
