Cofiniteness of generalized loca cohomology modules with respect to a system of ideals

Let $R$ be a commutative Noetherian ring, $\mathrm{\Phi }$ a system of ideals of $R$ and $M,X$ two $R$-modules. In this paper, we study the Artinianness and cofiniteness of the module $H_{\mathrm{\Phi }}^i(M,X)$ which is an extension of the generalized local cohomology modules of Herzog.