Covering-based rough sets are important generalizations of the classical rough sets of Pawlak. In this paper, by means of j-neighborhoods, complementary j-neighborhoods and j-adhesions, we build some new different types of j-covering approximations based rough sets and study related properties. Also, we explore the relationships between the considered j-covering approximations and investigate the properties of them. Using different neighborhoods, some different general topologies are generated as topologies induced from a binary relation. Finally, an interesting application of the new types of covering-based rough sets to the rheumatic fever is given.
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