One-to-one correspondence between fuzzifying topologies and fuzzy preorders

This paper is devoted to the discussion of the relationship between fuzzifying topologies and fuzzy relations. A saturated fuzzifying topology can be generated by a reflexive fuzzy relation; and conversely, a fuzzy preorder can be generated by a fuzzifying topology. In fact, there exists a one-to-one correspondence between the set of all saturated fuzzifying topologies and that of all fuzzy preorders.