  We study a quantum Bianchi type I model in which the dynamical variables of
the corresponding minisuperspace obey the generalized Heisenberg algebra. Such
a generalized uncertainty principle has its origin in the existence of a
minimal length suggested by quantum gravity and sting theory. We present
approximate analytical solutions to the corresponding Wheeler-DeWitt equation
in the limit where the scale factor of the universe is small and compare the
results with the standard commutative and noncommutative quantum cosmology.
Similarities and differences of these solutions are also discussed.
