Currently, coal is still the main energy source for China’s economic development, and the environmental issues caused by coal consumption have aroused widespread concern. Predicting and analyzing coal consumption will help to formulate a higher level of energy consumption planning and economic development strategy. The main purpose of this study is to develop a new fractal time-series prediction (FTSP) model to predict coal consumption, providing reference for formulating effective energy consumption planning and economic development strategies. Hurst index is an important indicator of whether time-series data have long memory and fractal characteristics. This paper uses the rescaled range (R/S) method to calculate Hurst index of the coal consumption per-10000-Yuan-GDP (CC/GDP). The Hurst index is 0.8025, exceeding 0.5, indicating that the time-series data CC/GDP has a long memory and fractal characteristic. Based on this, this paper uses the FTSP model to predict China’s coal consumption (CC/GDP). The prediction results show that the FTSP model accurately predicted China’s coal consumption with a relative error rate (RER) of less than 5% and a mean absolute percentage error (MAPE) of 6.62%. The model predicts a decrease in China’s coal consumption from 0.25 tons of standard coal in 2021 to 0.11 tons of standard coal in 2030, a decrease of 44%. To sum up, the FTSP model provides a new and accurate way to predict coal consumption, and the results suggest that China’s coal consumption is sustainable and will decrease significantly in the coming years. This study has important implications for energy consumption planning and economic development strategies.

The study of coal consumption has become a focus of academic attention due to ecological and environmental concerns. This study proposed a method to evaluate sustainability for coal consumption by using a multiple-attribute decision-making (MADM) model. The data used are from the China Statistical Yearbook and the China Energy Statistical Yearbook over the years. The MADM model consists of attributes (standards), their importance weights, and alternatives. The comprehensive evaluation system for the sustainability of coal consumption, which was composed of four first-grade indicators including coal strength (CS), energy dependency (ED), social development level (SL), and population size (PS) and their corresponding 20 second-grade indicators, was included in the MADM model as attributes (standards). The importance weight of the attributes was determined by the entropy weight method (EWM) and the analytic hierarchy process (AHP), while the comprehensive evaluation of the sustainability of coal consumption in China over the years was considered as an alternative. The evaluation indices of four first-grade indicators were obtained through multiobjective optimization, and then through the weights and evaluation indices of the four first-grade indicators, multiobjective optimization was carried out for the overall objective of the comprehensive evaluation of the sustainability of coal consumption over the years, and the comprehensive evaluation indices of the sustainable development of coal consumption over the years were obtained. The results show that China’s coal consumption is sustainable, with the composite assessment index rising from 0.058 in 2011 to 0.837 in 2021, an increase of 13.4 times.