Grey numbers facilitate the representation of uncertainty not only for elements of a set, but also the set itself as a whole. This paper utilizes the notion of possibility degree from grey system theory coupled with the idea of dominance relation and partial order set (poset) from rough theory to represent uncertain information in a manner that maintains the degree of uncertainty of information for each tuple of the original data. Concept lattices of grey information system are constructed and a decision-making algorithm that combines with grey relational grade is described. A case study is used to demonstrate the supplier selection problem applying the proposed method. The research has concluded that the method is appropriate to use.