In this paper, we propose MVN-ELSDeCS, which is a combination of VAE, a dimensionality reduction network, and MVN-XCSR, an XCSR extended to a distributional representation. In addition, additional learning of high-dimensional data with XCS is performed to reduce the information loss in learning caused by dimensionality reduction. We applied the proposed method to the benchmark problem of 10-class classification of handwritten digit images, and the experimental results have the following implications: 1) MVN-XCSR, which is a component of MVN-ELSDeCS, not only shows higher classification performance from the early stage of training in the dimensionally compressed latent space, but also 2) the reconstructed rules generated by MVN-ELSDeCS shows higher classification performance for the original high-dimensional data. Furthermore, 3) by applying additional learning with XCS to the reconstructed rules, the classification accuracy of rules for the 10-class classification task was significantly improved.