Generalized Closed Fuzzy Sets: A Unified Approach

Our system in this research depends on using the idea of the generalized closed sets in ordinary topological spaces for identification of the generalized closed fuzzy sets with its different types. Also trying for elucidation of the equivalent topological characters to transfer it to the fuzzy setting and elucidation of new results and theories, which we did not get before. We studied these types of the generalized closed fuzzy sets in one united study by entering, what we call, the closed fuzzy sets where and belong to the family and represent the type of fuzzy closure operator and the fuzzy open set respectively. In similar way, we united the study of different notions of fuzzy mappings. This study is characterized by the flexability where it is possible to enter new types or characters for all those types in the future by using the five different types of fuzzy closure operators and open fuzzy sets.