  Using the open quantum system approach applied to the neutrino system, we
derive three generations neutrino probability formulae considering the
oscillation induced by mass plus quantum decoherence contributions.
  The introduction of these dissipative effects is done through the quantum
dynamical semigroup formalism. In addition to the theoretical interest of the
approach, at least from the completeness point of view, this extension of the
formalism to the three flavors, provide us with a direct application: we can
analyze qualitatively the consistency of the two generation pure decoherence
solution to the atmospheric neutrino problem, accommodated within this enlarged
scheme, with the mean tendencies observed for some of the current neutrino
experimental data. This study was performed based on different choices of the
$3 \times 3$ mixing matrix selected in order to adjust the $P_{\nu_{\mu} \to
\nu_{\mu}}$ to the same form it has for the decoherence solution in two
generations. Our qualitative tests for decoherence with three neutrinos show a
clear incompatibility between neutrino data and the theoretical expectations.
