This paper, considers the fuzzy topological subsets, fuzzy topological spaces and introduces a novel concept of fuzzy Hausdorff space and fuzzy manifold space in this regards. Based on these concepts, we present a concept of fuzzy metric Hausdorff spaces and fuzzy metric manifold spaces via the notations of KM-fuzzy metric spaces.
This study, generalises the concept of fuzzy metric space to union and product of fuzzy metric spaces in classical logic and in this regard investigates the some product of fuzzy metric fuzzy manifold spaces. We apply the notation of valued-level subsets and make a relation between of topological space, Husdorff space, manifold space and fuzzy topological space, fuzzy Husdorff space and fuzzy manifold space. In final, we extended the fuzzy topological space, fuzzy Husdorff space and fuzzy manifold space to fuzzy metric topological space, fuzzy metric Husdorff space and fuzzy metric manifold space
Indeed, this study analyses the notation of fuzzy metric manifold based on valued-level subset.