Let $𝔞$ be an ideal of Noetherian local ring $(R,𝔪)$ and $M$ a finitely generated $R$-module of dimension $d$. In this paper we investigate the Artinianness of formal local cohomology modules under certain conditions on the local cohomology modules with respect to $𝔪$. Also we prove that for an arbitrary local ring $(R,𝔪)$ (not necessarily complete), we have ${\mathrm{Att}}_R\left({𝔉}_{𝔞}^d\left(M\right)\right)=\mathrm{Min}\mathrm{V}\left({\mathrm{Ann}}_R{𝔉}_{𝔞}^d\left(M\right)\right).$

Let $ℐ$ be a set of ideals of a commutative Noetherian ring $R$. We use the notion of $ℐ$-closure operation which is a semiprime closure operation on submodules of modules to introduce the class of $ℐ$-Laskerian modules. This enables us to investigate the set of associated prime ideals of certain $ℐ$-closed submodules of local cohomology modules.