In this thesis, a fuzzy metric space approach is considered for construction, analysis and approximation of sets and images, which may exhibit fractal characteristics. Many authors have introduced the concept of fuzzy metric spaces in different ways. We introduce in this work a new fuzzy metric space (space of fuzzy points), and use it to construct the fuzzy fractal space, then study some properties in term of their completeness since this property is important to ensure the existence of a fixed point for the family of continuous mappings. These mappings have proved to satisfy some generalizations of the contraction condition and constituted the iterative function system component, which is a method of generating fractals. The main aim of this thesis is to provide a generalization to the theory of fuzzy metric space to construct a new space that represents the finite Cartesian product of fuzzy fractal spaces called multi-fuzzy fractal space. Then the thesis discusses and proves its properties beginning with its completeness and going in the direction of ensuring the existence of a fixed point on it. Some implementation of the method of Iterated Function Systems (IFS) to grey level range [0,1] is generalized to method of Iterated Fuzzy Set Systems (IFZS), has been done.