In this paper a new method for training single-model and multi-model fuzzy classifiers incrementally and adaptively is proposed, which is called FLEXFIS-Class. The evolving scheme for the single-model case exploits a conventional zero-order fuzzy classification model architecture with Gaussian fuzzy sets in the rules antecedents, crisp class labels in the rule consequents and rule weights standing for confidence values in the class labels. In the multi-model case FLEXFIS-Class exploits the idea of regression by an indicator matrix to evolve a Takagi-Sugeno fuzzy model for each separate class and combines the single models' predictions to a final classification statement. The paper includes a technique for increasing the prediction quality, whenever a drift in a data stream occurs. An empirical analysis will be given based on an online, adaptive image classification framework, where images showing production items should be classified into good or bad ones. This analysis will include the comparison of evolving single- and multi-model fuzzy classifiers with conventional batch modelling approaches with respect to achieved prediction accuracy on new online data. It will also be shown that multi-model architecture can outperform conventional single-model architecture (`classical' fuzzy classification models) for all data sets with respect to prediction accuracy. (c) IEEE Press