Recent advances in weakly multi-label learning (MLL) have demonstrated impressive potential in multi-label classification tasks. Unfortunately, collecting multi-labels for each instance proves to be time-consuming and labor-intensive, since these MLL methods requires the assessment of all the candidate labels. To alleviate this challenge, a novel labeling setting termed Determined Multi-Label Learning is proposed, aiming to effectively reduce the cost for browsing labels in multi-label tasks. In this setting, each training instance is associated with a determined multi-label, which indicates whether the instance contains the provided class label. Besides, each instance only need to be determined once, which significantly reduce the annotation cost of the labeling task for multi-label datasets. In this paper, we theoretically derive an risk-consistent estimator to learn from these determined-labeled training data. Additionally, we introduce a similarity-based prompt learning method, which minimizes the risk-consistent loss of large-scale pre-trained models to learn a supplemental prompt with richer semantic information. Extensive experimental validation underscores the efficacy of our approach. Our code is available at the link: https://github.com/WilsonMqz/DMLL