Rough I-??-Statistical Convergence of Order ? in Neutrosophic Normed Spaces

Abstract

In this paper, we investigate rough I[jls-end-space/]- ? ?[jls-end-space/]-statistical convergence of order ? in neutrosophic normed spaces and establish several fundamental structural properties of the associated limit sets. We first show that the family { Lj } j ? 0 of rough statistical limit sets is monotone with respect to the roughness parameter j[jls-end-space/], and each Lj is convex under mild monotonicity assumptions on the neutrosophic components. For j = 0[jls-end-space/], rough convergence reduces to the classical I[jls-end-space/]- ? ?[jls-end-space/]-statistical convergence of order ?[jls-end-space/], ensuring that the limit set is a singleton. We further demonstrate that the rough limit set is always neutrosophically closed and neutrosophically convex, highlighting its stability under both topological and geometric operations. A characterization of strong I[jls-end-space/]- s t ? ? ?[jls-end-space/]-boundedness is obtained via the non-emptiness of the rough limit set. In addition, we introduce the notion of Ij ? s t ? ? ?[jls-end-space/]-cluster points and prove that every rough limit point is a cluster point, while the cluster set remains neutrosophically closed. Finally, we show that this convergence framework unifies several classical notions of statistical and ideal convergences as particular cases. © The Author(s) 2026