Evolving fuzzy systems (EFSs) are a type of adaptive fuzzy rule-based systems which can self-adapt both their structures and parameters simultaneously. However, the existing EFSs suffer from two drawbacks: 1) classical EFSs usually use all input features to model systems, resulting in lengthy fuzzy rules; 2) some redundant information in fuzzy rules may hinder high generalization. To address these two issues, a promising method is proposed in this paper by combining very sparse random projection (VSRP) with a class of EFSs based-on data clouds, called VSRP-AnYa-EFS. The proposed method introduces: 1) a random sparse-Bernoulli (RSB) matrix based-on VSRP is utilized to compress the lengthy antecedent part into a tighter form, triggering a feature-reduction mechanism. By employing VSRP in RSB matrix, some redundant information in fuzzy rules can be filtered; 2) Local learning is used for consequent parameter optimization to suit decoupled behavior of rules after redundant information between rules is deleted. By adopting VSRP and local learning, the proposed VSRP-AnYa-EFS owns a compact structure and fast learning speed. Numerical examples presented in this paper demonstrate that the proposed method can significantly reduce training time from hours to minutes while the accuracy can be improved up to 5%.