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Economic and environmental benefits are the most important in the operation of community integrated energy systems (CIES), modeled as a bi-objective optimization problem. In the case of the uncertainties from loads and renewable energy generators, the effectiveness of the operation strategies may be degraded in the practical applications of CIES. In this paper, an improved triangle splitting based bi-objective optimization method is proposed to search for the Pareto optimal solution of the CIES operation. The general preference of decision-makers in practical applications is utilized in the search process to reduce the detailed search interval and consequently improve the optimization efficiency. In addition, a bi-objective uncertain optimization framework is established for the economic-environmental operation of the CIES under uncertainties. The correlation between uncertainties is considered to generate the operation scenarios, in which the solution probability function is employed to determine the final operation strategy with robustness. A comprehensive case study is conducted based on a practical CIES in China, proving the feasibility and effectiveness of the proposed methods.