Similarity of binary relations based on <Emphasis Type="Italic">L</Emphasis>-fuzzy topologies

Binary relations play an important role in rough set theory. This paper investigates the similarity of binary relations based on L-fuzzy topologies, where L is a boolean algebra. First, rough approximations based on a boolean algebra are proposed through successor neighborhoods on binary relations. Next, L-fuzzy topologies induced by binary relations are investigated. Finally, similarity of binary relations is introduced by using the L-fuzzy topologies and the fact that every binary relation is solely similar to some preorder relation is proved. It is worth mentioning that similarity of binary relations are both originated in the L-fuzzy topology and independent of the L-fuzzy topology.