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Multi-label classification has attracted much attention in the machine learning community to address the problem of assigning single samples to more than one class at the same time. We propose an evolving multi-label fuzzy classifier (EFC-ML) which is able to self-adapt and self-evolve its structure with new incoming multi-label samples in an incremental, single-pass manner. It is based on a multi-output Takagi-Sugeno type architecture, where for each class a separate consequent hyper-plane is defined. The learning procedure embeds a locally weighted incremental correlation-based algorithm combined with (conventional) recursive fuzzily weighted least squares and Lasso-based regularization. The correlation-based part ensures that the interrelations between class labels, a specific well-known property in multi-label classification for improved performance, are preserved properly; the Lasso-based regularization reduces the curse of dimensionality effects in the case of a higher number of inputs. Antecedent learning is achieved by product-space clustering and conducted for all class labels together, which yields a single rule base, allowing a compact knowledge view. Furthermore, our approach comes with an online active learning (AL) strategy for updating the classifier on just a number of selected samples, which in turn makes the approach applicable for scarcely labelled streams in applications, where the annotation effort is typically expensive. Our approach was evaluated on several data sets from the MULAN repository and showed significantly improved classification accuracy compared to (evolving) one-versus-rest or classifier chaining concepts. A significant result was that, due to the online AL method, a 90\% reduction in the number of samples used for classifier updates had little effect on the accumulated accuracy trend lines compared to a full update in most data set cases.