A grey rough set model based on (α,β) grey similarity relation

Combining the methods of rough set theory and grey system theory and by introducing the grey number concept, the conventional incomplete information system method is extended and a kind of (alpha, beta)-grey similarity relation GSIM_{(alpha, beta)} of grey information system is proposed, then the model of grey rough set based on the (alpha, beta)-grey similarity relation is established and investigation is made in the related foundational theories. Methods are proposed to describe the positive, boundary and negative regions and the reduction of grey decision-making table in the grey rough set by the recognition degree mode of grey theory, and a solution to the problem of incoherence is brought forward in the grey decision-making table from the angle of recognition degree mode. Example shows that this kind of model is more intuitive and rational. It breaks through the limitation of the study on conventional rough set theory which is restricted to the classic relations.