A generalized framework for $\varsigma$-neutrosophic fuzzy metric spaces and related fixed-point theorems

This paper introduces $\varsigma$-neutrosophic fuzzy metric spaces ( $\varsigma$-NFMSs), a significant generalization of neutrosophic fuzzy metric spaces (NFMSs). By extending the parameter space from a single dimension $(0,\mathrm{\infty })$ to a multi-dimensional vector space $(0,\mathrm{\infty }{)}^{\varsigma }$, this framework offers enhanced flexibility for modeling complex systems where uncertainty depends on multiple factors simultaneously. The study investigates the topological properties of $\varsigma$-NFMSs, rigorously proving that their topology is first-countable and that the associated space is Hausdorff. Furthermore, a generalized fixed-point theorem is established within this new framework, extending previous results in NFMSs.