Fuzzy orders and fuzzifying topologies

The paper presents the essential connections between fuzzy preorders and fuzzifying topologies. In detail, we establish systematic procedure indicating how fuzzifying topologies are induced from fuzzy preordered relations on a set X, and conversely, we will answer the problem that the specialization order can be induced by a fuzzifying topology on a set X. Moveover, a powerful method generating fuzzy preordered relations is obtained.