Neighbourhood rough set theory has proven already, as an efficient tool for knowledge discovering from heterogeneous data. However, some types of the data are incomplete and noisy in practical environments, such as signal analysis, fault diagnosis etc. To solve this problem, a universal neighbourhood rough sets model (variable precision tolerance neighbourhood rough sets [VPTNRS] model) is proposed based on a tolerance neighbourhood relation and the probabilistic theory. The proposed model can be inducing a family of much more comprehensive information granules to characterize arbitrary concepts in complex universe. In this paper, we discussed the properties of the model as well as some important relevant theorems are also introduced and proved. Furthermore, a heuristic heterogeneous feature selection algorithm is given based on the model. The experimental results with 10 choices University of California Irvine (UCI) standard data sets showed that the universal model performed well both in feature selection and classification, especially in incomplete environment.