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 $I^{*}-liminf$.

In this work, we analyze the Fibonacci difference matrix and use it to develop new sequence spaces in the neutrosophic normed spaces (NNS). This study also includes a detailed analysis of several important properties of these spaces, including their linearity property, first countability and Hausdorffness.

The proposed article aims to study some topological properties of triple real sequence spaces with respect to fuzzy-anti-normed linear space (FANLS). In this work the algebra of fuzzy I?-limit and fuzzy I? -anti limit, where 0 < ? < 1 and I is an ideal on N3, of triple real sequences along with an interesting example have been studied. Furthermore, the completeness of a special kind of sequence space with respect to fuzzy anti-norm has been examined.

In this paper, for fuzzy metric spaces we will attempt to demonstrate some novel fixed-point theorems that is common. To support our findings with evidence, we employ the concept of compatibility. The previous review found several useful mutual fixedpoint theorems for metric and fuzzy metric spaces. Our results greatly expand and strengthen these theorems. Reconsideration of fuzzy metric spaces is done by this study so that fuzzy scalars are utilized to construct fuzzy metric spaces rather than real numbers or fuzzy numbers. In contrast to the preceding work, which defined fuzzy metric spaces using fuzzy or real numbers, this definition uses fuzzy numbers. It has been demonstrated that any complete regular metric space can, under certain conditions, complete fuzzy metric space are given. In addition, we provide evidence that the fuzzy metric spaces generate fuzzy topology that is specified in this study and is consistent with previously presented fuzzy topologies. In the coming years, these findings will pave the way for additional research into imperfect optimization and pattern recognition.