One of the considerable subjects in mathematics is the study of topology. Deducing topology from arbitrary binary relations has enticed the attention of many researchers. So, we devote this article to generate some kinds of topologies from ideals and Ej-neighborhoods which are induced from any binary relation. We define new types of approximations and accuracy measures from these topologies and then compare them with their counterparts induced directly from Ej-neighborhoods and ideals. Also, we show that the approximations and accuracy measures given, herein, are better than those introduced in some previous studies under any arbitrary relation.