The definition of fuzzy length space on fuzzy set in this research was introduced after the studies and discussion of many properties of this space were proved, and then an example to illustrate this notion was given. Also the definition of fuzzy convergence, fuzzy bounded fuzzy set, and fuzzy dense fuzzy set space was introduced, and then the definition of fuzzy continuous operator was introduced.

In this paper we recall the definition of fuzzy length space on a fuzzy set after that we recall basic definitions and properties of this space. Then we prove the fixed fuzzy point theorems for a fuzzy complete fuzzy length spaces on a fuzzy set. Are finite dimensional fuzzy length spaces simpler than infinite dimensional ones in this direction we proved some properties that does not satisfied in the infinite case.