  One-loop radiative corrections will lead to a small difference between the
matter potentials developed by $\nu_\mu^{}$ and $\nu_{\tau}$ when they travel
in a medium. By including such radiative corrections, we derive the exact
expressions of the corresponding effective mass-squared differences and the
moduli square of the lepton flavor mixing matrix elements $|\widetilde
U_{\alpha i}^{}|^2$ (for $\alpha=e,\mu,\tau $ and $i=1,2,3$) in matter in the
standard three-flavor mixing scheme and focus on their asymptotic behaviors
when the matter density is very big (i.e., the matter effect parameter $A\equiv
2\sqrt{2} G_{\rm F}^{} N_e^{}E$ is very big). Different from the non-trivial
fixed value of $|\widetilde U_{\alpha i}^{}|^2$ in the $A\to \infty$ limit in
the case without radiative corrections, we get $|\widetilde U_{\alpha
i}^{}|^2=0~{\rm or}~1$ under this extreme condition. The radiative corrections
can significantly affect the lepton flavor mixing in dense matter, which are
numerically and analytically discussed in detail. Furthermore, we also extend
the discussion to the $(3+1)$ active-sterile neutrino mixing scheme.
