Model transparency, label correlation learning and the robust-ness to label noise are crucial for multilabel learning. However, few existing methods study these three characteristics simultaneously. To address this challenge, we propose the robust multilabel Takagi-Sugeno-Kang fuzzy system (R-MLTSK-FS) with three mechanisms. First, we design a soft label learning mechanism to reduce the effect of label noise by explicitly measuring the interactions between labels, which is also the basis of the other two mechanisms. Second, the rule-based TSK FS is used as the base model to efficiently model the inference relationship be-tween features and soft labels in a more transparent way than many existing multilabel models. Third, to further improve the performance of multilabel learning, we build a correlation enhancement learning mechanism based on the soft label space and the fuzzy feature space. Extensive experiments are conducted to demonstrate the superiority of the proposed method.