A proper representation of the uncertainty involved in a prediction is an important prerequisite for the acceptance of machine learning and decision support technology in safety-critical application domains such as medical diagnosis. Despite the existence of various probabilistic approaches in these fields, there is arguably no method that is able to distinguish between two very different sources of uncertainty: aleatoric uncertainty, which is due to statistical variability and effects that are inherently random, and epistemic uncertainty which is caused by a lack of knowledge. In this paper, we propose a method for binary classification that does not only produce a prediction of the class of a query instance but also a quantification of the two aforementioned sources of uncertainty. Despite being grounded in probability and statistics, the method is formalized within the framework of fuzzy preference relations. The usefulness and reasonableness of our approach is confirmed on a suitable data set with information about patients suffering from chest pain.

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In this paper, we introduce a fuzzy extension of a class of measures for comparing clustering structures, namely measures that are based on the number of concordant and the number of discordant pairs of data points. This class includes the well-known Rand index but also commonly used alternatives, such as the Jaccard measure. In contrast to previous proposals, our extension exhibits desirable metrical properties. Apart from elaborating on formal properties of this kind, we present an experimental study in which we compare different fuzzy extensions of the Rand index and the Jaccard measure.

Supplementary data are available at Bioinformatics online.

So-called classifier chains have recently been proposed as an appealing method for tackling the multi-label classification task. In this paper, we analyze the influence of a potential pitfall of the learning process, namely the discrepancy between the feature spaces used in training and testing: While true class labels are used as supplementary attributes for training the binary models along the chain, the same models need to rely on estimations of these labels when making a prediction. We provide first experimental results suggesting that the attribute noise thus created can affect the overall prediction performance of a classifier chain.