Rough I -γτ-Statistical Convergence of Order α in Neutrosophic Normed Spaces

In this paper, we investigate rough I - γ τ -statistical convergence of order α in neutrosophic normed spaces and establish several fundamental structural properties of the associated limit sets. We first show that the family L j j ≥ 0 of rough statistical limit sets is monotone with respect to the roughness parameter j, and each L j is convex under mild monotonicity assumptions on the neutrosophic components. For j = 0, rough convergence reduces to the classical I - γ τ -statistical convergence of order α, 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 - s t γ τ α -boundedness is obtained via the non-emptiness of the rough limit set. In addition, we introduce the notion of I j − s t γ τ α -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.