The authors discuss the relationship between fuzzifying topologies in the sense of [\textit{U. Höhle}, J. Math. Anal. Appl. 78, 659--673 (1980; Zbl 0462.54002)], [\textit{M. Ying}, Fuzzy Sets Syst. 39, No.~3, 303--321 (1991; Zbl 0718.54017)] and fuzzy preorders. A systematic procedure for inducing fuzzifying Alexandrov topologies from fuzzy preordered relations and vice versa for inducing a fuzzy preorder from a fuzzifying topology are presented. The former is based on the notion of fuzzyfied set of all upper crisp subsets. If the preorder is a fuzzy equivalence then the induced fuzzifying topology is pseudo-discrete. The authors also prove that the fuzzy preorder determined by the latter procedure is a specialization order of the fuzzifying topological space. Although some possible applications of the results presented in the paper are mentioned there are no examples illustrating the proposed procedures.