  Neutrino properties can be constrained by the detection of ultra-high energy
cosmic neutrinos (UHECNs). By using the updated global fitting results of
neutrino mixing parameters, we present predictions on the neutrino flavor
ratios at the Earth from three possibly astrophysical sources. Comparing with
the latest IceCube data, we find that the normal hierarchy (NH) and inverted
hierarchy (IH) cases from the initial ratios
$\phi_{\nu_e}^0:\phi_{\nu_{\mu}}^0:\phi_{\nu_{\tau}}^0=$1:2:0 and 0:1:0 are
compatible with the data in the standard neutrino oscillation scenario. We also
examine the neutrino flavor ratios in a neutrino decay scenario beyond the
standard model, and introduce the special case that two mass eigenstates of
neutrinos, i.e., $\nu_1$ and $\nu_2$, are degenerated. We find that the IH case
and the degenerate NH case from the 1:2:0 and 0:1:0 sources are still
permissible with the IceCube data within the $3\sigma$ error range. The general
constraints only rely on the neutrino mixing and oscillation framework are also
discussed.
