Abstract: The grey attribute group decision-making procedures based on grey system theory,in which the attribute values are interval grey numbers with parially known weight information is explored.The definition of deviation degree between two interval grey numbers is given from the essence of interval grey numbers as well as the concepts and formulas for individual imagined optimum vector and degree of group integrated grey incidence.Therefore the incidece degree coefficient formula is constructed from an analytical technique based on deviation degree for interval grey numbers and a minimax regret-based approach is proposed to compare and rank this interval integrated grey incidence degree.Finally an example is used to illustrate the rationality of this grey attribute group decision-making method and the validity of the algorithms developed in this paper.