Filter structure on fuzzy topological spaces

In the thesis, filters in fuzzy topological spaces is worked. In order for these concepts to be understood in fuzzy topological spaces, firstly the concept and features of the filter are briefly mentioned in classical topological spaces. Moreover, it is aimed to provide the understanding of the space studied by giving the definition of the indefinite topological space and talking about its properties. Then, in the indefinite topological spaces, the filter concepts are given in a pedagogical order and it is aimed to understand these concepts thoroughly. The concept of filters in fuzzy the topological space where there is a lot of work in topology, has created a wide field of study. Many filter concepts have been defined on fuzzy topological spaces. R. Lowen, W. Gahler, M. H. Burton, M. Muraleetharan, Vicente and Aranguren are some mathematicians working on this subject. In this thesis, on the fuzzy topological spaces respectively the four main filter concepts are considered: prefilter, generalized filter, I-filter and supra fuzzy filter. The aim of the study is to provide a regular and understandable resource for the people who will work in this subject by giving the concept of filter which varies in fuzzy topological spaces in order. For this reason, general information about this topic is collected from specific articles, theses and books and this information is given in a sequential manner.