T. Tanushri

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 $I^{*}-liminf$.