Data uncertainty is inherent in many real-world applications and poses significant challenges for accurate time series predictions. The interval type 2 fuzzy neural network (IT2FNN) has shown exceptional performance in uncertainty modelling for single-step prediction tasks. However, extending it for multi-step ahead predictions introduces further issues in uncertainty handling as well as model interpretability and accuracy. To address these issues, this paper proposes a new selforganizing interval type-2 fuzzy neural network with multiple outputs (SOIT2FNN-MO). Differing from the traditional six-layer IT2FNN, a nine-layer network architecture is developed. First, a new co-antecedent layer and a modified consequent layer are devised to improve the interpretability of the fuzzy model for multi-step time series prediction problems. Second, a new link layer is created to improve the accuracy by building temporal connections between multi-step predictions. Third, a new transformation layer is designed to address the problem of the vanishing rule strength caused by high-dimensional inputs. Furthermore, a two-stage, self-organizing learning mechanism is developed to automatically extract fuzzy rules from data and optimize network parameters. Experimental results on chaotic and microgrid prediction problems demonstrate that SOIT2FNN-MO outperforms state-of-the-art methods, by achieving a better accuracy ranging from 1.6% to 30% depending on the level of noises in data. Additionally, the proposed model is more interpretable, offering deeper insights into the prediction process.