This paper introduces rough I₂-lacunary statistical convergence for complex uncertain double sequences (CUDS), extending concepts of rough convergence, rough lacunary statistical convergence, and rough I₂-convergence. We explore this notion across four aspects of uncertainty: almost surely, measure, mean, and distribution. Additionally, we investigate rough I₂-lacunary statistical convergence in p-distance and metric spaces for CUDS. The study illustrates the interconnectedness of these convergence concepts and offers observations on their relationships.

In this paper, the notion of (`N, pn )-summability to generalize the concept of statistical convergence is used. We call this new method weighted statistically convergence. We also establish its relationship with statistical convergence, (C, 1)-summability and strong (`N, pn )-summability.

In this paper we investigate the notion of I-statistical convergence and introduce I-st limit points and I-st cluster points of real number sequence and also studied some of its basic properties.