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The concept, which we will be considered in this book, is the so called "fuzzy sets" which is totally different from the classical concept which is called "a crisp set". The recent concept is introduced by Zadeh in 1965, in which he defines fuzzy sets as a class of objects with a continuum of grades of membership and such a set is characterized by a membership function that assigns to each object a grade of membership ranging between zero and one.In (1968) Chang introduced the definition of fuzzy topological spaces and extended in a straight forward manner some concepts of crisp topological spaces to fuzzy topological spaces.