The tasks of making decisions on risk assessment, depending on the conditions of uncertainty, are divided into two types: decision-making tasks under conditions where the initial data are stochastic; decision-making tasks under conditions when the initial data are of a non-stochastic nature, and the necessary confidence limits for the parameters of the processes under investigation are unknown or unclear. In problems of the second type, risks are manifested to a greater extent than the first, since in solving problems it is necessary to take into account not only statistical uncertainty, but also linguistic. At the same time, one should consider risk as information uncertainty and fuzziness of the system and its individual elements. The measure of this uncertainty determines the measure of danger, possible damage, loss from the realization of some decision or event. Proceeding from this, it is necessary to allocate the basic property of risk: the risk takes place only in relation to the future and is inseparably connected with forecasting, and hence with decision-making on risk assessment. In the article the construction of soft risk assessment models based on fuzzy inference rules and neural networks have been discussed for learning fuzzy knowledge bases. The essence of training is in the selection of such parameters of membership functions that minimize the difference between the results of neuron-fuzzy approximation and the actual behavior of the object.