About the Completeness of Fuzzy Metric Spaces

The objective of this work may be oriented toward two objectives.The first objective is to study fuzzy set theory, as well as some of its basic algebraic properties and theoretical results.The second objective is to study D-metric spaces and M-fuzzy metric spaces, and some of their properties. Also, this objective includes the study of complete fuzzy metric spaces using M-fuzzy distance function. In addition, some additional results are presented and proved in this work.