Summary: This paper presents a novel hybrid interval type-2 neuro-fuzzy inference system, with automatic learning of all its parameters, to handle uncertainty. This new model, called hierarchical type-2 neuro-fuzzy BSP model (T2-HNFB), combines the paradigms of the type-2 fuzzy inference systems and neural networks with recursive partitioning techniques (binary space partitioning - BSP). The model is able to automatically create and expand its own structure, to reduce limitations on the number of inputs and to extract fuzzy linguistic rules from a dataset, as well as to efficiently model and manipulate most types of uncertainty existing in real situations. In addition, it provides an interval for its output, which can be regarded as a measure of uncertainty and constitutes important information for real applications. In this context, this model overcomes the limitations of the conventional type-2 and type-1 fuzzy inference systems. Experimental results show that the results provided by the T2-HNFB model are close to and in several cases better than the best results supplied by the other models used for comparison.