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In this paper, we propose a novel design of evolving fuzzy classifiers (EFC) for handling on-line multi-class classification problems in a data streaming context. Therefore, we exploit the concept of all-pairs (AP) aka all-versus-all classification using binary classifiers for each pair of classes. This benefits from less complex decision boundaries to be learned opposed to direct multi-class approach and achieves a higher efficiency in terms of incremental training time than one-versus-rest classification techniques. For the binary classifiers, we apply fuzzy classifiers with singleton class labels in the consequences as well as TS fuzzy models for conducting regression on [0; 1] for each class pair. Both are evolved and incrementally trained in a datastreaming context, yielding a permanent update of the whole all-pairs collection of classifiers, thus being able to properly react on dynamic changes in the streams. The classification phase considers a novel strategy by using the preference levels of each pair of classes collected in a preference relation matrix and performing a weighted voting scheme on this matrix. This is done by investigating the reliability of the classifiers in their predictions: 1.) integrating the degree of ignorance on samples to be classified as weights for the preference levels; 2.) new conflict models used in the single binary classifiers and when calculating the final class response based on the preference relation matrix. The advantage of the new evolving fuzzy classifier concept over single model (using direct multi-class classification concept) and multi model architectures (using one-versus-rest classification concept) will be underlined by empirical evaluations and comparisons at the end of the paper based on high-dimensional real-world multi-class classification problems. The results also show that integrating conflict and ignorance concepts into the preference relations can boost classifier accuracies.