Similarity of fuzzy relations based on fuzzy topologies induced by fuzzy rough approximation operators

This paper studies similarity of fuzzy relations which is based on fuzzy topologies induced by fuzzy rough approximation operators. First, fuzzy topologies induced by fuzzy rough approximation operators are investigated and the concept of similarity of fuzzy relations is introduced. Next, it is proved that every fuzzy relation is uniquely similar to some fuzzy preorder relation and a characteristic condition for fuzzy relations to be transitive is established. Finally, algebraic structures on similarity of fuzzy relations are obtained.