Novel Insights into the Theory of Sequence Spaces for Fuzzy Numbers via Bessel Functions

This paper explores new directions in the study of sequence spaces for fuzzy numbers by introducing and examining Bessel statistical convergence and strong Bessel summability. We establish key inclusion relations and build a theoretical framework that deepens the understanding of convergence and summability in fuzzy settings. As an important application, we extend the classical fuzzy Korovkin-type theorem through Bessel statistical convergence, showing greater flexibility and wider applicability than existing results. Our framework is particularly effective for sequences that fail to converge in the classical sense but display statistical convergence, as illustrated with Bessel-perturbed approximation operators. In addition, we investigate the fuzzy rate of Bessel statistical convergence, providing a way to measure the speed of convergence and offering new insight into approximation processes in fuzzy contexts. Examples and visualizations are included to demonstrate the practical value of our results in areas such as uncertainty modeling, control systems, and computational mathematics.