Kernelized fuzzy rough sets

Kernel machines and rough sets are two classes of popular learning techniques. Kernel machines enhance traditional linear learning algorithms to deal with nonlinear domains by a nonlinear mapping, while rough sets introduce a human-like manner to deal with uncertainty in learning. Granulation and approximation play a central role in rough sets based learning and reasoning. Fuzzy granulation and fuzzy approximation, which is inspired by the ways in which humans granulate information and reason with it, are widely discussed in literatures. However, how to generate effective fuzzy granules from data has not been fully studied so far. In this work, we integrate kernel functions with fuzzy rough set models and propose two types of kernelized fuzzy rough sets. Kernel functions are employed to compute the fuzzy T-equivalence relations between samples, thus generate fuzzy information granules of the approximation space, and then these fuzzy granules are used to approximate the classification based on the conception of fuzzy lower and upper approximations.