Ankle assist devices frequently experience gait phase transitions and foot-ground contact changes during walking, leading to fluctuations in human-machine coupling stiffness and interaction forces, which can cause contact impacts and affect the stability of the assist output. To reduce interaction impacts and improve system compliance, this paper employs a series elastic actuator (SEA) to drive the ankle joint. Addressing the issue that SEA dynamic lag makes it difficult to balance interaction compliance and rapid torque response, an SEA-based ankle assist device is designed, and a dynamic model considering elastic energy storage dynamics and human-machine coupling disturbances is established. Based on this, a composite strategy integrating interval type-II fuzzy impedance control and non-singular fast terminal sliding mode force control is proposed: interval type-II fuzzy impedance control enables online adaptive parameter adjustment to dynamically match human-machine coupling impedance characteristics; combined with non-singular fast terminal sliding mode force control, the tracking accuracy of the assist torque and the system's disturbance rejection capability are improved. The proposed method is validated through simulation and walking experiments. Simulation results show that the proposed control strategy can reduce the peak human-machine interaction force by approximately 5.16% during gait switching, thereby improving interaction compliance. The walking experiment results showed that the wearer's gastrocnemius muscle electromyographic activation decreased by approximately 12.22%, verifying the effectiveness of the proposed control strategy in improving human-computer interaction performance.