Deep neural networks (DNNs) have been shown to perform well on exclusive, multi-class classification tasks. However, when different classes have similar visual features, it becomes challenging for human annotators to differentiate them. When an image is ambiguous, such as a blurry one where an annotator can't distinguish between a husky and a wolf, it may be labeled with both classes: {husky, wolf}. This scenario necessitates the use of composite set labels. In this paper, we propose a novel framework called Hyper-Evidential Neural Network (HENN) that explicitly models predictive uncertainty caused by composite set labels in training data in the context of the belief theory called Subjective Logic (SL).By placing a Grouped Dirichlet distribution on the class probabilities, we treat predictions of a neural network as parameters of hyper-subjective opinions and learn the network that collects both single and composite evidence leading to these hyper-opinions by a deterministic DNN from data.We introduce a new uncertainty type called vagueness originally designed for hyper-opinions in SL to quantify composite classification uncertainty for DNNs.Our experiments prove that HENN outperforms its state-of-the-art counterparts based on four image datasets.The code and datasets are available at: https://shorturl.at/dhoqx.