  In this article, we tentatively assign the $Z_c^\pm(3900)$ to be the
diquark-antidiquark type axialvector tetraquark state, study the hadronic
coupling constants $G_{Z_cJ/\psi\pi}$, $G_{Z_c\eta_c\rho}$, $G_{Z_cD
\bar{D}^{*}}$ with the QCD sum rules in details. We take into account both the
connected and disconnected Feynman diagrams in carrying out the operator
product expansion, as the connected Feynman diagrams alone cannot do the work.
Special attentions are paid to matching the hadron side of the correlation
functions with the QCD side of the correlation functions to obtain solid
duality, the routine can be applied to study other hadronic couplings directly.
We study the two-body strong decays $Z_c^+(3900)\to J/\psi\pi^+$,
$\eta_c\rho^+$, $D^+ \bar{D}^{*0}$, $\bar{D}^0 D^{*+}$ and obtain the total
width of the $Z_c^\pm(3900)$. The numerical results support assigning the
$Z_c^\pm(3900)$ to be the diquark-antidiquark type axialvector tetraquark
state, and assigning the $Z_c^\pm(3885)$ to be the meson-meson type axialvector
molecular state.
