  Fuzzy rough sets are well-suited for working with vague, imprecise or
uncertain information and have been succesfully applied in real-world
classification problems. One of the prominent representatives of this theory is
fuzzy-rough nearest neighbours (FRNN), a classification algorithm based on the
classical k-nearest neighbours algorithm. The crux of FRNN is the
indiscernibility relation, which measures how similar two elements in the data
set of interest are. In this paper, we investigate the impact of this
indiscernibility relation on the performance of FRNN classification. In
addition to relations based on distance functions and kernels, we also explore
the effect of distance metric learning on FRNN for the first time. Furthermore,
we also introduce an asymmetric, class-specific relation based on the
Mahalanobis distance which uses the correlation within each class, and which
shows a significant improvement over the regular Mahalanobis distance, but is
still beaten by the Manhattan distance. Overall, the Neighbourhood Components
Analysis algorithm is found to be the best performer, trading speed for
accuracy.
