Similarity of binary relations based on rough set theory and topology: an application for topological structures of matroids

摘要

In this paper, we propose an integration of rough sets, matroids and topology to exploit the advantages of three theories. First, weconsider topologies induced by binary relations and illustrate that binary relations can be researched by means of topology. Next, similarity of binary relations based on rough set theory and topology is introduced and the fact that every binary relation is solely similar to some preorder relation is proved. Finally, as an application of the similarity, topological structures of matroids are given.