The hybrid grey attribute group decision-making problem that the attribute weights and authoritative weights
are known between two continuous linguistic grades is discussed, in which the attribute values are interval grey numbers
and linguistic grades, and a new decision-making method is proposed in the paper. The method is that each decision-maker
gives whitenization of each interval grey number based on his/her preference and belief structure form of qualitative attribute
values, and each decision-maker’ grade belief structure decision matrix and group grade belief structure decision matrix can
be determined. A new method for solving group aggregation weight is proposed. By using the analytical ER algorithm,
belief degrees of each alternative belonging to each linguistic grade are obtained. Expected utilities of each alternative and
method for ranking interval numbers are utilized to rank the alternatives. An example shows the feasibility and effectiveness
of the proposed method.