The ground subsidence due to underground mining can be regarded as a fuzzy event. This subsidence will take place at a fuzzy probability

and so the theory of fuzzy measures can be applied to predicting the ground subsidence and stability of building foundations. Based on results of the statistical analysis of a large amount of measured data in mining engineerings; the fundamental fuzzy model of ground subsidence is established by using the theory of fuzzy mathematics. The agreement of the theoretical results with the field measurements shows that our model is satisfactory and the formulae obtained are valid and thus can be effectively used for predicting the stability of building foundations on mined-out areas.