Fuzzy-rough sets play an important role in dealing with imprecision and uncertainty for discrete and real-valued or noisy data. However, there are some problems associated with the approach from both theoretical and practical viewpoints. These problems have motivated the hybridisation of fuzzy-rough sets with kernel methods. Existing work which hybridises fuzzy-rough sets and kernel methods employs a constraint that enforces the transitivity of the fuzzy T-norm operation. In this paper, such a constraint is relaxed and a new kernel-based fuzzy-rough set approach is introduced. Based on this, novel kernel-based fuzzy-rough nearest-neighbour algorithms are proposed. The work is supported by experimental evaluation, which shows that the new kernel-based methods offer improvements over the existing fuzzy-rough nearest neighbour classifiers. The abstract goes here.