The $mathfrak{a}$-Filter grade of an ideal $mathfrak{b}$ and $(mathfrak{a},mathfrak{b})$-$mathrm{f}$-modules

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.