Boolean lattices of $n$-multiply $\Omega$-bicanonical Fitting classes

We describe the $n$-multiply $\Omega$-bicanonical Fitting classes with Boolean lattice of Fitting subclasses. In particular, it is shown that in this case a Fitting class is directly decomposable with the use of the set of all atoms of its lattice. Here the notion of a direct decomposition plays the key role. Therefore we study direct decompositions separately and consider $\Omega$-foliated Fitting classes with more general directions.