Neighbourhood-assignment attribute reduction based on general binary relations

Attribute reduction based on discernibility matrix is one of the important issues in rough set theory. It is also vital to study attribute reduction based on general binary relations. In this paper, the concept of neighborhood-assignment consistent set of attribute reduction based on binary relations is first presented and some of its main properties are discussed. Then, a new attribute reduction method based on a neighborhood-assignment discernibility matrix is proposed. Finally, by applying the proposed attribute reduction method in a practical problem related to water pollutions, some main factors polluting water quality are obtained. The practical example shows that the proposed method is effective.