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In addition to its important economic value, carbon trading is also an important tool in international politics and diplomacy. Carbon price forecast accuracy has far-reaching implications for economic development and the environment. Few existing studies have been more accurate in predicting carbon prices over longer periods. In this paper, the incremental Gaussian nonlinear trend fuzzy granulation method and the Gaussian nonlinear trend fuzzy granulation method are innovatively proposed to predict carbon prices. This study first converts carbon prices into incremental granulation time series. A time-varying core line is added to produce nonlinear trend granulation on the foundation of linear trend granulation. The nonlinear trend and residual information are then predicted using the DeeAR network, respectively, and the final prediction result is obtained by adding the predicted values for each. Moreover, a new evaluation index, the comprehensive evaluation of RMSE, MAE, and MAPE as three indicators, is proposed to consider the accuracy of the evaluation index more comprehensively and reliably. The results show that the prediction method has the smallest error in long-term prediction compared with other models. The daily closing price datasets of carbon exchanges published in Shenzhen and Beijing are used to validate the efficacy of this methodology. • A modified Gaussian nonlinear trend that can better fit the actual data is proposed. • Incremental Gaussian nonlinear trend fuzzy granulation method with F test is proposed. • A new evaluation index is proposed to make the prediction result more interpretable. [ABSTRACT FROM AUTHOR]