  Let $\mathfrak{a},\mathfrak{b}$ be two ideals of a commutative noetherian
ring $R$ and $M$ a finitely generated $R$-module.~We continue to study
$\textrm{f}\textrm{-}\mathrm{grad}_R(\mathfrak{a},\mathfrak{b},M)$ which was
introduced in [Bull. Malays. Math. Sci. Soc. 38 (2015) 467--482], some
computations and bounds of
$\textrm{f}\textrm{-}\mathrm{grad}_R(\mathfrak{a},\mathfrak{b},M)$ are
provided.~We also give the structure of
$(\mathfrak{a},\mathfrak{b})$-$\mathrm{f}$-modules,~various properties which
are analogous to those of Cohen Macaulay modules are discovered.
