Abstract: As a carrier of urban energy generation, transport and consumption, the urban integrated energy system(UIES) requires sufficient flexibility in its operation to balance various uncertain fluctuations. A flexibility index for dispatch based on the fluctuation range of uncertainty is proposed from the definition of flexibility. To reduce the decision conservatism of using traditional interval numbers to describe uncertainties due to the loss of probabilistic information, a multi-band interval number(MBIN) considering correlation is proposed to describe the uncertainties. A continuous cumulative distribution function is obtained from the historical data and interpolation method. A multi-objective interval optimization dispatch model for UIES is proposed to minimize the operating cost and maximize the available uncertain fluctuation range of outdoor temperature and illumination intensity. The interval possibility method is used to handle the constraints containing traditional interval numbers and MBIN considering correlation, and transforms the original model into a deterministic multi-objective mixed-integer linear optimization model. Using a method for directly solving the compromise optimal solution of the multi-objective optimization problem, the model is further transformed into a single-objective mixed-integer linear programming model, which can be solved efficiently. Finally, an actual UIES with agricultural-industrial-commercial campus case is analyzed, and the computational results validate the effectiveness of the proposed model and solution method.