Collaborative filtering (CF) stands as a cornerstone in recommender systems, yet effectively leveraging the vast reservoir of unlabeled data presents a persistent challenge. Current research endeavors to address the challenge of unlabeled data by extracting a subset closely approximating negative samples. Regrettably, the remaining data are overlooked, failing to fully integrate this valuable information into the construction of user preferences. To address this gap, we introduce a novel positive-neutral-negative (PNN) learning paradigm. PNN introduces a neutral class, encompassing intricate items challenging to categorize directly as positive or negative samples. By training a model based on this triple-wise partial ranking, PNN offers a promising solution to learning complex user preferences. Through theoretical analysis, we connect PNN to one-way partial AUC (OPAUC) to validate its efficacy. Implementing the PNN paradigm is, however, technically challenging because: (1) it is difficult to classify unobserved items into neutral or negative in the absence of supervisory signals; (2) there does not exist any loss function that can handle set-level triple-wise ranking relationships. To address these challenges, we propose a semi-supervised learning method coupled with a user-aware attention model for knowledge acquisition and classification refinement. Additionally, a novel loss function and two-step centroid ranking approach enable handling set-level rankings. Extensive experiments on four real-world datasets demonstrate that, when combined with PNN, a wide range of representative CF models can consistently and significantly boost their performance. Our code is publicly available at https://anonymous.4open.science/r/PNN-RecBole-4E04.