The outbreak of epidemic has had a big impact on the investment market of China. Facing the turbulence in the investment market, many enterprises find it difficult to judge the development prospects of investment projects and make the right investment decisions. The three-way decisions offer a novel study perspective to solve this problem. Then the developed model is applied to select the investment projects. Firstly, some relevant attributes of the project are described with the double hierarchy hesitant fuzzy linguistic term sets. And a double hierarchy hesitant fuzzy linguistic information system is constructed for each project. Secondly, the weights of attributes are determined with the Choquet integral method. And the closeness degree calculated by Choquet-based bi-projection method is taken as the conditional probability that the project will be profitable. Next, considering the influence of the bounded rationality of decision makers, the threshold parameters are calculated based on prospect theory. Finally, the decision results about investment projects during four stages are deduced based on the principle of maximum-utility, which demonstrates the practicability and effectiveness of the proposed model.