  The total available sample of fast radio bursts (FRBs) has been growing
steadily in recent years, facilitating the study of FRBs from a statistical
point of view. At the same time, the classification of FRBs is currently an
imperative issue. We propose that the brightness temperature of bursts can
serve as an ideal criterion for classification. In this work, we gather the
available data for all localized FRBs and we find a positive relation between
the intrinsic pulse width and burst energy, $T_{\rm i}\propto E_\nu^{0.25}$,
for three repeating FRBs that is similar to that of our previous work using FRB
20121102A data alone. The critical line $T_{\rm B,cri}$ is found to vary for
different FRBs, which may reflect the differences in source properties. This
relation can put strong constraints on mainstream radiation mechanisms. It is
evident that neither the coherent curvature radiation or synchrotron maser
radiation have the capability to reach the high brightness temperature required
to reproduce this relation.
