  It is proposed that supersymmetry (SUSY) maybe used to understand fermion
mass hierarchies. A family symmetry Z_{3L} is introduced, which is the cyclic
symmetry among the three generation SU(2) doublets. SUSY breaks at a high
energy scale ~ 10^{11} GeV. The electroweak energy scale ~ 100 GeV is
unnaturally small. No additional global symmetry, like the R-parity, is
imposed. The Yukawa couplings and R-parity violating couplings all take their
natural values which are about (10^0-10^{-2}). Under the family symmetry, only
the third generation charged fermions get their masses. This family symmetry is
broken in the soft SUSY breaking terms which result in a hierarchical pattern
of the fermion masses. It turns out that for the charged leptons, the tau mass
is from the Higgs vacuum expectation value (VEV) and the sneutrino VEVs, the
muon mass is due to the sneutrino VEVs, and the electron gains its mass due to
both Z_{3L} and SUSY breaking. The large neutrino mixing are produced with
neutralinos playing the partial role of right-handed neutrinos. |V_{e3}| which
is for nu_e-nu_{tau} mixing is expected to be about 0.1. For the quarks, the
third generation masses are from the Higgs VEVs, the second generation masses
are from quantum corrections, and the down quark mass due to the sneutrino
VEVs. It explains m_c/m_s, m_s/m_e, m_d > m_u and so on. Other aspects of the
model are discussed.
