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In this paper, a special class of neighborhood systems, called reflexive 1-neighborhood systems is introduced, properties of neighborhood and approximation operators are studied, and their connections are examined. In addition, this paper discussed incomplete systems from view of point of information view, and in order to measure uncertainty of knowledge and roughness of rough set in incomplete information systems knowledge, the indiscernibility relation in classical rough set theory is necessary to be extended to some more general relations. Furthermore, information entropy is introduced to study the rough entropy of knowledge and the roughness of the rough set based on covering granules, which are described with reflexive 1-neighborhood systems. Finally, a new kind of measurement about the roughness of knowledge and rough set is proposed.
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