T-similarity of fuzzy relations and related algebraic structures

In this paper, we show that fuzzy Alexandrov topologies can be induced by fuzzy relations. The concept of T-similarity of fuzzy relations is introduced. Variations of the same fuzzy relation are investigated. The fact that every fuzzy relation is solely T-similar to some T-preorder fuzzy relation is proved. A characteristic condition for fuzzy relations to be T-transitive is established. These results illustrate that fuzzy relations can be studied by means of topology. Moreover, algebraic structures based on T-similarity of fuzzy relations are obtained.