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The analysis and prediction of agent trajectories are crucial for decision-making processes in intelligent systems, with precise short-term trajectory forecasting being highly significant across a range of applications. Agents and their social interactions have been quantified and modeled by researchers from various perspectives; however, substantial limitations exist in the current work due to the inherent high uncertainty of agent intentions and the complex higher-order influences among neighboring groups. SocialMOIF is proposed to tackle these challenges, concentrating on the higher-order intention interactions among neighboring groups while reinforcing the primary role of first-order intention interactions between neighbors and the target agent. This method develops a multi-order intention fusion model to achieve a more comprehensive understanding of both direct and indirect intention information. Within SocialMOIF, a trajectory distribution approximator is designed to guide the trajectories toward values that align more closely with the actual data, thereby enhancing model interpretability. Furthermore, a global trajectory optimizer is introduced to enable more accurate and efficient parallel predictions. By incorporating a novel loss function that accounts for distance and direction during training, experimental results demonstrate that the model outperforms previous state-of-the-art baselines across multiple metrics in both dynamic and static datasets.