<p>This paper introduces a novel arctangent-based interval-valued intuitionistic fuzzy entropy function designed to address multi-attribute group decision-making problems, particularly in situations where attribute weights are either completely unknown or only partially known. The proposed entropy function computes the objective weights of the attributes and, by integrating these with subjective weights, derives a comprehensive weight. This methodology effectively addresses uncertainties and the incomplete nature of weight information in decision-making processes. Furthermore, the paper extends the bidirectional projection method to the interval intuitionistic fuzzy context, developing a multi-attribute decision-making model that integrates the arctangent-based interval-valued intuitionistic fuzzy entropy and the bidirectional projection method. Finally, a series of comparative experiments are conducted to validate the effectiveness and robustness of the proposed entropy function and bidirectional projection method in multi-attribute decision-making.</p>