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In order to solve the decision-making problem that the attributive values are internal grey numbers and the attributive weights are unknown, this study develops a novel decision-making method based on prospect theory for environments with interval grey numbers. First, interval grey numbers are employed to characterize uncertain preference information, whereas scenario-specific reference points and distance measures are utilized to compute positive and negative ideal solutions, followed by the construction of a prospect value function. Then, an information entropy optimization method is established to determine optimal attribute weights (with "optimal" explicitly defined as the weight configuration that maximizes decision consistency under entropy constraints), enabling subsequent alternative ranking through comprehensive prospect value evaluation. Finally, the feasibility and effectiveness of the model were empirically validated by applying it to renewable energy investment decision-making. The results conclusively demonstrate that the proposed approach provides an effective solution for complex multi-attribute decision-making under uncertainty, while exhibits substantial practical value in real-world applications.