The present research introduces a novel concept termed “neutrosophic fuzzy metric space”, which extends the traditional metric space framework by incorporating the notion of neutrosophic fuzzy sets. A thorough investigation of various structural and topological properties within this newly proposed generalization of metric space has been conducted. Additionally, counterparts of well-known theorems such as the Uniform Convergence Theorem and the Baire Category Theorem have been established for this generalized metric space. Through rigorous analysis, a detailed understanding of its fundamental characteristics has been attained, illuminating its potential applications and theoretical significance.

The primary objective of the paper is to present the Banach contraction theorem in soft fuzzy metric spaces while taking into consideration a restriction on the soft fuzzy metric between the soft points of the absolute soft set. A new altering distance function, namely the $\mathsf{\Psi }$-contraction function, is introduced on soft fuzzy metric spaces, and some fixed point results are proven by considering soft mappings that comprise $\mathsf{\Psi }$-contraction with the continuity of soft t-norm. In addition to that, some illustrations are supplied for the support of the established soft fuzzy Banach contraction theorem and fixed point results over $\mathsf{\Psi }$-contraction mappings. The obtained results generalize and extend some well-known results present in the literature on fixed point theory.

In this study, we introduce fuzzy weak -contraction and Suzuki-type fuzzy weak -contraction and employ these to prove some fuzzy fixed point results for fuzzy mappings in the setting of metric spaces, which is followed by an example to support our claim. Next, we deduce some corollaries and fixed point results for multivalued mappings from our main result. Finally, as an application of our result, we provide the existence of a solution for a Fredholm integral inclusion.