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Type-1 fuzzy system is able to provide an inference mechanism to reason with imprecise information, but it is unable to do so under linguistic and numerical uncertainties. While the incorporation of interval type-2 fuzzy set can offer a model for handling further uncertainty, it is relatively difficult to extract the footprint of uncertainty information. In addition, fuzzy systems are unable to automatically acquire the linguistic rules to model the problem. In this paper, an interval type-2 fuzzy neural model named Interval type-2 Neural Fuzzy Inference System (IT2NFIS) is proposed, to automatically generate the linguistic model with interval type-2 fuzzy sets and thus their faced uncertainties. The structure identification algorithm is based on Piaget's cognitive view of an action-driven cognitive development in human. IT2NFIS is evaluated on Nakanishi data sets and the results show that IT2NFIS is comparable if not superior to other models.