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For the economic operation of a blast furnace, the thermal state change of a blast furnace hearth (BFH), often represented by the change of the silicon content in hot metal, needs to be strictly monitored and controlled. For these purposes, this paper has taken the tendency prediction of the thermal state of BFH as a binary classification problem and constructed a ν-support vector machines (SVMs) model and a probabilistic output model based on ν-SVMs for predicting its tendency change. A highly efficient ordinal-validation algorithm is proposed to combine with the F-score method to single out inputs from all collected blast furnace variables, which are then fed into the constructed models to perform the predictive task. The final predictive results indicate that these two models both can serve as competitive tools for the current predictive task. In particular, for the probabilistic output model, it can give not only the direct result whether the next thermal state will get hot or cool down but also the confidence level for this result. All these results can act as a guide to aid the blast furnace operators for judging the thermal state change of BFH in time and further provide an indication for them to determine the direction of controlling blast furnaces in advance. Of course, it is necessary to develop a graphical user interface in order to online help the plant operators.