Building a model to predict the state of slag on coal-fired boilers is a good way to optimize the coal combustion and reduce the risk of boiler slag. This paper built new models based on vague sets to predict the state of slag on coal-fired boilers, in which there were six input vectors, which were softening temperature, SiO2-Al2O3 ratio, alkali-acid ratio, percentage of silicon content, the dimensionless average temperature furnace and the dimensionless inscribed circle diameter furnace, and one output vectors, which was slagging degree. Two methods, which were based on the sense of distance and symmetric fuzzy cross entropy, were proposed to calculate the similarity between vague sets. 10 coal burning boilers were selected as known samples and the feasibility of the new methods was proved by the result of predicting the state of slag on the four coal burning boilers from Jilin heat and power plant, Xinli power plant, Jinzhou power plant and Qinhuangdao power plant. Through predicting and determining, it proves that the two pattern recognition models are high in prediction accuracy. Compared with the normal method, it is easier for operators to predict, determine the slagging state and reduce disturbance as far as possible. Besides, a prediction system has been developed by object-oriented high-level language accordingly.