A generalized framework for ς-neutrosophic fuzzy metric spaces and related fixed-point theorems

Abstract

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, infinity) to a multi-dimensional vector space (0, infinity)& 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.