The shadowed set-based rough fuzzy clustering (SRFCM) methods have shown great performance on the data with outliers. But for the data with non-spherical clusters, the SRFC approaches cannot produce good results. The reason is the SRFCM, just like classical fuzzy c-means algorithms, works on the original data space and assures the linear separability of different clusters. The kernel methods can be combined with fuzzy clustering to deal with the non-spherical problem, but the size of kernel matrix is the square of the number of the input data, which makes the kernel fuzzy clustering is not suitable for very large data. But if we approximate the kernel space by using Fourier random feature mappings, the SRFC can be directly applied over the random features generated by data. This approach combines the advantages of SRFCM in handling outliers and the random features in processing non-spherical clusters. The experimental results show good performance of the SRFCM in the random feature space.