A Framework for I*-Statistical Convergence of Fuzzy Numbers

Abstract

In this study, we investigate the concept of I*-statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship between I*-statistical convergence and classical convergence, and the algebraic properties of I*-statistically convergent sequences. We also introduce the concept of I*-statistical pre-Cauchy and I*-statistical Cauchy sequences and explore its connection to I*-statistical convergence. Our results show that every I*-statistically convergent sequence is I*-statistically pre-Cauchy, but the converse is not necessarily true. Furthermore, we provide a sufficient condition for an I*-statistically pre-Cauchy sequence to be I*-statistically convergent, which involves the concept of I*−liminf.