We show ideal convergence ( $I$-convergence), ideal Cauchy ( $I$-Cauchy) sequences, $I^{\ast }$-convergence and $I^{\ast }$-Cauchy sequences for double sequences in fuzzy metric spaces. We define the $I$-limit and $I$-cluster points of a double sequence in these spaces. Afterward, we provide certain fundamental properties of the aspects. Lastly, we discuss whether the phenomena should be further investigated.

In this paper, we introduce and study the concept of rough statistical convergence for double sequences in L-fuzzy normed spaces. We define the rough statistical limit points of a double sequence and prove that the set is closed and convex. In addition, we define rough statistical cluster points of a double sequence, and we prove that this set is closed. Afterward, we investigate the relationships among rough statistical convergence for double sequences, related notions such as rough statistical boundedness, and rough statistical Cauchy-type conditions.