Breast cancer is one of the most common cancers in women worldwide and the leading cause of death in women. Medical experts use histopathological images to diagnose breast cancer, but such analysis for the effective diagnosis or detection of breast cancer is challenging. Therefore, we propose a vector deep fuzzy neural network (VDFNN) to classify breast cancer effectively and automatically from histopathological images. The VDFNN model uses four sets of vector product and pooling layers to extract features and retain important feature information. Then, a feature fusion layer uses global average pooling to reduce the dimension of the extracted feature information. Finally, a fuzzy neural network performs breast cancer classification. The VDFNN model parameters are selected using the trial-and-error method. However, we also propose the Taguchi-VDFNN (T-VDFNN), which employs the Taguchi method to determine the optimal combination of model parameters. The experimental breast cancer classification accuracy of the proposed VDFNN was 92.18%. After the application of the Taguchi method to identify the optimal parameter combination, the experimental accuracy of the proposed T-VDFNN model was 94.37%, 2.19 percentage points higher than that of the basic VDFNN model.