As the cost of data labeling continues to escalate, research on feature selection for a partially labeled multiset-valued decision information system (p-MSVDIS) has emerged as a core challenge in the field of data mining. Information entropy, as an uncertainty measurement tool, can be used for feature selection via global equivalence relations. However, it fails to capture features within local data regions. Furthermore, in partially labeled scenarios, its limitations in dealing with missing labels cause poor accuracy in feature selection. In contrast, local conditional entropy can accurately characterize the discriminative ability of features in local regions by quantifying the information of the dataset. To address the problem of feature selection in a p-MSVDIS, this paper proposed two algorithms for feature selection in a p-MSVDIS. First, we utilized the Hellinger distance in a p-MSVDIS to define the tolerance classes of different attributes. Second, we introduced local conditional entropy and designed two feature selection algorithms for a p-MSVDIS with predicted labels. Finally, comparative experimental results demonstrated that the proposed algorithms significantly improved classification performance and reduced redundant features in partially labeled data scenarios.