A new fuzzy metric space are introduced in this work. It is used to construct the fuzzy fractal space. Its properties in term of their completeness are studied 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 the method of generating fractals. The main aim of this book 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. Its properties are discussed and proved beginning with its completeness and going in the direction of ensuring the existence of a fixed point. 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).

I am an Associ. Prof. in the Applied Mathematics Department-University of Technology-Baghdad- Iraq. I joined this department since 1989. My Ph.D. degree is in mathematics and computer application sciences 2003. From 2008-2010, I took the position of postdoctoral at University Putra Malaysia. I am the author of numerous technical papers since 1991.

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