  It has been found that the quantum-to-classical transition can be observed
independent of macroscopicity of the quantum state for a fixed degree of
fuzziness in the coarsened references of measurements. Here, a general
situation, that is the degree of fuzziness can change with the rotation angle
between two states (different rotation angles represent different references),
is researched based on the reason that the fuzziness of reference can come from
two kinds: the Hamiltonian (rotation frequency) and the timing (rotation time).
Our results show that, for the fuzziness of Hamiltonian alone, the degree of
fuzziness for reference will change with the rotation angle between two states
and the quantum effects can still be observed no matter how much degree of
fuzziness of Hamiltonian; for the fuzziness of timing, the degree of coarsening
reference is unchanged with the rotation angle. Moreover, during the rotation
of the measurement axis, the decoherence environment can also help the
classical-to-quantum transition due to changing the direction of measurement
axis.
