The distribution of heavy metals among the residues is a major problem in coal-fired power stations. An exact collection of their concentration in coal of different origin is hardly possible. Uncertainties, which nearly all operating parameters in a power station are afflicted with, can be quantified and their influence on the balance errors can be described by the application of fuzzy numbers. So-called membership functions allow to approximate the composition of fuels. Transfer factors, which have been determined experimentally in the power station, enable to calculate the fuzzy material flow and the fuzzy composition of all residues. Different methods have been applied to convert the membership function of compositions to sharp numbers, which have been compared with measured data.