Integrated demand response (IDR) can improve the operating economy, flexibility and reliability of a park integrated energy system (PIES), and realize the synergistic benefits of both supply and demand. Given the uncertainty of IDR in the actual operation of a PIES, an optimal operation model of the PIES considering the uncertainty of IDR is proposed. First, the uncertainty models of shiftable electric load and transferable load response based on consumer psychology principles are established. Then, according to the ambiguity of thermal user temperature perception and the thermal inertia of heating buildings, an adjustable thermal load response model considering the uncertainty of solar radiation intensity is established. An optimal operation model of the PIES considering the uncertainty of the IDR with the goal of maximizing the total revenue of the integrated energy aggregator is constructed, and is solved by the enhanced-interval linear programming method. Simulation results show that IDR can effectively improve the operating economy and renewable energy consumption of the PIES. The effect of IDR can be displayed more objectively and accurately by considering the uncertainty of IDR, and it can provide auxiliary decision-making for the formulation of a PIES operational strategy. This work is supported by the Science and Technology Program of Sichuan Province (No. 2021YFSY0019).