In view of the fact that a multiple attribute group decision-making problem arises where attribute values are provided as interval-valued intuitionistic fuzzy numbers, a new method of attitudes concentrated order has been proposed, taking into consideration the situations where the decision maker,s risk preferences and attribute weights are not completely determined. Firstly, a comparison has been made of the evaluation values in the decision matrix according to the defined score function, followed by an arrangement of the schemes in linear sequence. Secondly, the attribute weights can be obtained with a model built on the basis of this new ranking method, and an ultimate ordering scheme can be worked out by taking advantage of the weighted average operator to aggregate all the schemes. Finally, a numerical example is given to verify the feasibility of this method.