L-Fuzzy Co-Alexandrov Topological Spaces

Firstly, we present some characterizations of L-fuzzy poset and their corresponding proofs. Then, we give the definition of L-fuzzy upper set and prove its related properties. Next, we define the concept of L-fuzzy Co-Alexandrov topological space on an L-fuzzy poset (X, e). We further study the properties of L-fuzzy Co-Alexandrov topological space and equivalent characterizations, which are generalizations of the Alexandrov topological space on a poset (X, sqsub) in the classical topological space theory. Finally, we establish the relationships of L-fuzzy poset, L-fuzzy upper set and L-fuzzy Co-Alexandrov topological space. These relationships make clear that we can use L-fuzzy poset, L-fuzzy upper set to construct the L-fuzzy Co-Alexandrov topogical space. All the theories we proposed to provide a general theoretical framework for the study of the fuzzy data types, fuzzy relations and fuzzy approximation operators in information systems and database technology.