Categorical study of fuzzy topological structures

Abstract

In order to study the control problems of complicate systems and dealing with fuzzy information ,L.A.Zadeh introduced fuzzy set theory in 1965, describing fuzziness mathematically for the first time. Fuzzy set extended the basic mathematical concept- Set (crisp set). Fuzzy topological structures is just a kind of mathematics developed on fuzzy sets. In mathematics literature, extensive study of fuzzy topological spaces and fuzzy uniform structures is done by various researchers. Therefore, it seems natural to find the common context, as wide as possible and interrelation between these structures. Throughout this dissertation we have adopted the categorical point of view for some fuzzy topological structures and fuzzy frame structures. The language of category theory has proved to be an adequate tool in the study of the relation between structures.