Application of neutrosophic normed spaces to analyze the convergence of sequences involving neutrosophic operators

This work introduces the concept of $ \alpha\beta $-Rough-I-statistical convergence of order $ \eta $, focusing on its application within neutrosophic analysis, a system that helps handle vague and uncertain information in mathematics. The study explores the behavior of mathematical operators under this convergence and emphasizes their utility in addressing problems in uncertain settings. Furthermore, we propose the notion of $ \alpha\beta $-Rough-I-statistical-cluster points in neutrosophic normed spaces and its connection to the limit set of $ \alpha\beta $-Rough-I-statistical convergence of order $ \eta $ is analyzed in the context of neutrosophic normed spaces. Furthermore, numerical examples are included to illustrate the practical significance of the developed approach.