On the Relationship Among Relational Categories of Fuzzy Topological Structures

Relational variants of categories of Čech closure or interior L-valued operators, categories of L-fuzzy pretopological and L-fuzzy co-pretopological operators, category of L-valued fuzzy relation, categories of upper and lower F-transforms and the category of spaces with fuzzy partitions are introduced. The existence of relationships defined by functors among these categories are investigated and a key role of a relational category of spaces with fuzzy partitions is described.