Intuitionistic smooth topology

This study consists of five parts. In the first part of the study, the historical process of study is was first considered. In the second part, the definition of fuzzy topological spaces is given, which refer to general properties of fuzzy clusters.In addition, this section introduces the concept of ıntuitionistic fuzzy sets. In the third part of thesis, various theorems have been proved by using some features of the concept of ıntuitionistic fuzzy sets. In the fourth part of the thesis, definition and properties of topological space in the sense of Sostak are given. Finally, in this section, fuzzy (r,s)-semiopen cluster and fuzzy (r,s)- semiclosed cluster definitious are examined. In the last part of the thesis, discussion and conclusion part are given. Key Words : Fuzzy topology,intuitionistic fuzzy sets, intuitionistic fuzzy topological space in Sostak'ın sense fuzzy (r,s)-semiopen cluster and fuzzy (r,s)-semiclosed cluster.