With respect to the different confidence on the decision result from the different decision-makers to the hybrid multi-attribute group decision-making under risk, two approaches to group decision-making based on prospect theory and improved projection theory are proposed. Firstly, an array is established to record the evaluation result from the group decision-makers. Mixed decision data in the array is changed into the triangular fuzzy number. Considering the confidence degree from single decision-maker to evaluation result, the group decision information is aggregated and the weights of attributes are calculated. Two methods are proposed to rank the alternatives, which are comprehensive prospect value from the prospect theory and relative closeness degree from the improved projection method. Finally, an application case is given to demonstrate the reasonability and effectiveness of the proposed approach.