Evolving intelligent system (EIS) is a machine learning algorithm, specifically designed to deal with learning from large data streams. Although the EIS research topic has attracted various contributions over the past decade, the issue of uncertainty, temporal system dynamic, and system order are relatively unexplored by existing studies. A novel EIS, namely evolving type-2 recurrent fuzzy neural network (eT2RFNN) is proposed in this paper. eT2RFNN features a novel recurrent network architecture, possessing double local recurrent connections. It generates a generalized interval type-2 fuzzy rule, where an interval type-2 multivariate Gaussian function constructs the rule premise, and the rule consequent is crafted by the nonlinear wavelet function. eT2RFNN adopts an open structure, where it can start learning process from scratch with an empty rule base. Fuzzy rules can be automatically generated according to degree of nonlinearity data stream conveys. It can performs a rule base simplification procedure by pruning and merging inactive, outdated and overlapping rules. eT2RFNN can deal with the high dimensionality problem, where an online dimensionality reduction method is integrated in the training process. The efficacy of the eT2RFNN has been numerically validated using two real-world data streams, where it provides high predictive accuracy, while retaining low complexity.