Although fuzzy c-means algorithm has shown great capability to spherical clusters, it can not perform very well on non-spherical data sets yet. To deal with this problem, kernel-based fuzzy clustering has been presented by mapping data points into a high-dimensional Hilbert space with kernel functions. However, the computational complexity of kernel matrix is always quadratic, usually makes kernel fuzzy clustering non-scalable to large data sets. Recently, random features display a strong capability in approximating kernel functions while satisfying appropriate memory requirements. Therefore, we introduce two fuzzy clustering schemes in this paper based on random feature mapping and dimension reduction methods to approximate kernel fuzzy c-means clustering on general size data sets and one large data set. The clustering results illustrate the great potential of the proposed approaches.