  Distinct from the type of local realist inequality (known as the
Collins-Gisin-Linden-Massar-Popescu or CGLMP inequality) usually used for
bipartite qutrit systems, we formulate a new set of local realist inequalities
for bipartite qutrits by generalizing Wigner's argument that was originally
formulated for the bipartite qubit singlet state. This treatment assumes
existence of the overall joint probability distributions in the underlying
stochastic hidden variable space for the measurement outcomes pertaining to the
relevant trichotomic observables, satisfying the locality condition and
yielding the measurable marginal probabilities. Such generalized Wigner
inequalities (GWI) do not reduce to Bell-CHSH type inequalities by clubbing any
two outcomes, and are violated by quantum mechanics (QM) for both the bipartite
qutrit isotropic and singlet states using trichotomic observables defined by
six-port beam splitter as well as by the spin-$1$ component observables. The
efficacy of GWI is then probed in these cases by comparing the QM violation of
GWI with that obtained for the CGLMP inequality. This comparison is done by
incorporating white noise in the singlet and isotropic qutrit states. It is
found that for the six-port beam splitter observables, QM violation of GWI is
more robust than that of the CGLMP inequality for singlet qutrit states, while
for isotropic qutrit states, QM violation of the CGLMP inequality is more
robust. On the other hand, for the spin-$1$ component observables, QM violation
of GWI is more robust for both the type of states considered.
