Several Properties Of Fuzzy Metric Space

In this paper, based on the theory of fuzzy metric space, severalproperties of fuzzy metric space are concerned.Firstly, some preliminaries important definitions and lemmas that are fre-quently used in the remaining chapters are provided. Secondly, this paper studiesthe completions and properties on L -fuzzy metric spaces based on the L -fuzzymetric introduced by R.Saadati who generalizes fuzzy metric. It especially provesBaire theorem on L -fuzzy metric spaces. Moreover, some fixed point theoremsfor fuzzy mappings on complete fuzzy metric space are performed. Finally, thistreatise generalizes the Hausdorff fuzzy metric in the sense of J.Rodriguez-Lopezand S.Romaguera, and introduce a new M_∞-fuzzy metric. It is also concernedwith some properties of M_∞-fuzzy metric. Furthermore, underφ-contraction con-dition, in the fuzzy metric space, several fixed point theorems on fuzzy sets arediscussed.