Neural networks are currently popular learning models to represent and analyze data. We address two issues about that in this paper. On the one hand, the parameters between neurons are often restricted to be constants, which greatly limits the learning ability and reduces the robustness of the neural network. For that, it is necessary to make the parameters fuzzy. In this paper, we introduce the fuzzy set theory to neural networks where the parameters are expressed by fuzzy numbers. Meanwhile, the loss term and sparsity of the network become fuzzy. On the other hand, a user-defined weighting parameter need to be determined to keep the tradeoff between the fuzzy loss term and fuzzy sparsity. In order to solve the two issues simultaneously, the main contribution of this paper is to combine fuzzy set theory with multi-objective sparsity to apply to neural networks, for the first time, and propose a fuzzy multi-objective sparse feature learning (FMSFL) model, where a multi-objective optimization model is established, and reconstruction error and sparsity of fuzzy model are considered as two objectives. In the experiments, we demonstrate the effectiveness of our model, and both learning capability and robustness of the neural networks based on the proposed model are improved.
