To study the effect of different demand responses (DRs) on solving uncertainty, a multi-objective robust optimization model for a community virtual cloud power plant (CVCPP) is proposed based on the correlative confidence gap decision theory (CCGDT) and considering different DRs. Firstly, a CVCPP framework with multi-energy conversion equipment, multi-load DR, and a rapid energy scheduling information processing approach is proposed. Secondly, a two-layer community comprehensive demand response model is developed, which includes the CDR of CIES internal consumers and the CDR of the external energy network that connects to CIES. Thirdly, the CCGDT is presented using the confidence gap decision model and the time-varying Copula theory. A multi-objective robust economy-energy-environment optimization model is developed. Fourthly, the Pareto solution set is solved using the multi-objective grey wolf optimization algorithm. The full consistency method is employed to identify an optimal scheduling strategy for decision-makers. Finally, the model's validity is verified by a multi-scene case of a residential area. The results show that: 1) Whether uncertainty is considered or not, different DRs have varied effects on the results. Combination DR are better than single, and the same DR has different effects on different residents. 2) The multi-objective values improve after adopting the integrated energy system. The resident cost of various residents is decreased by 0.054%-12.07% when uncertainty is included. Meanwhile, the profit of energy providers is improved by 0.95%-10.98%, the carbon treatment amount is lowered by 26.85%-51.31%, and the renewable energy utilization rate is enhanced by 0.85%-7.94%. 3) The results with different significance have different robustness to uncertainty changes, and the greater the significance, the stronger the robustness. Therefore, the decision-maker can flexibly control the optimization result by setting the confidence of the target value. The model plays a good role in the economy-energy-environment aspects and provides a reference for community decision-makers to choose the comprehensive multi-objective energy scheduling strategy considering the uncertainty.