Analyzing the Limit Set of Rough Ideal ??-Statistical Convergence of Order ? in Lattice-Valued Fuzzy Normed Spaces

Abstract

This study introduces the framework of rough I-lambda gamma-statistical convergence of order & rhov; within the setting of L-fuzzy normed spaces (lattice-valued fuzzy normed spaces). This generalizes existing convergence notions by integrating ideal convergence (I), generalized sequence transformations (lambda gamma), an arbitrary order (& rhov;), and the concept of roughness (r). A primary focus is the characterization of the resulting rough limit set. We rigorously establish that, contrary to classical convergence, the limit is inherently a set. Furthermore, we prove that this limit set possesses key structural properties, specifically closure and convexity, under the topology induced by the L-fuzzy norm. Finally, we define the corresponding notion of I-lambda gamma-statistical cluster points of order & rhov; and elucidate the relationship between this set of cluster points and the rough limit set.