Concerning the rough ideal convergence of double sequences within the topology induced by a fuzzy 2-norm

Abstract

This research paper presents a thorough exploration of rough I2-convergence, rough I*2 -convergence, rough I2-limit points, and rough I2-cluster points for double sequences within a fuzzy 2-normed linear space. A key contribution is the proof of a specific decomposition theorem related to rough I2-convergence of double sequences. Additionally, we introduce the concepts of rough IE2 -double Cauchy sequences and I*,E2-double Cauchy sequences, alongside an exploration of their properties. Notably, our investigation establishes connections between the notion of rough ideal cluster points in a fuzzy 2-normed space and conventional criteria for ideal convergence, highlighting the interplay between these two seemingly distinct mathematical ideas. This study provides a comprehensive analysis of various aspects of rough convergence, the set of rough limit points, and rough cluster points in the context of sequences within fuzzy 2-normed spaces.