As an effective tool to deal with uncertain decision-making, three-way decisions (TWD) have gained wide attention in many applications. Decision-theoretic rough sets (DTRSs) as a classic model of TWD contain two key elements, i.e., conditional probability and loss functions. In this paper, we study the determination of these two elements in depth via the information interaction and modification strategy, and further propose a novel model of TWD. First, fuzzy c-means (FCM) is used to cluster the condition attribute information and loss function information, respectively. Considering the interaction of two types of information, we design the corresponding fusion tactic of these clustering results to get equivalent classes and develop a new calculation method of conditional probability. Then, we use probabilistic hesitant fuzzy sets (P-HFSs) to aggregate the loss functions of different members of the same equivalence class and get the probabilistic hesitant fuzzy elements (P-HFEs) loss functions. In this case, P-HFSs not only reflect the hesitant situation of decision-makers, but also depict the proportion of different opinions. Regarding P-HFEs loss functions, we also investigate the modification methods of its outliers in detail. Moreover, based on the P-HFEs loss functions, we propose TWD with probabilistic hesitant fuzzy decision-theoretic rough sets (P-HFDTRSs). Finally, in order to verify the effectiveness of our proposed method, we develop a series of comparative experiments and discuss the decision results on six UCI datasets.

作为处理不确定决策的有效工具，三向决策（TWD）在许多应用中得到了广泛关注。决策理论粗糙集（DTRS）作为 TWD 的经典模型包含两个关键要素，即条件概率和损失函数。在本文中，我们通过信息交互和修改策略深入研究了这两个元素的确定，并进一步提出了一种新的 TWD 模型。首先，使用模糊 c 均值 (FCM) 分别对条件属性信息和损失函数信息进行聚类。考虑到两类信息的相互作用，我们设计了这些聚类结果的相应融合策略以获得等价类，并开发了一种新的条件概率计算方法。然后，我们使用概率犹豫模糊集（P-HFSs）聚合同一等价类不同成员的损失函数，得到概率犹豫模糊元素（P-HFEs）损失函数。在这种情况下，P-HFSs 不仅反映了决策者的犹豫情况，还描绘了不同意见的比例。关于 P-HFEs 损失函数，我们还详细研究了其异常值的修改方法。此外，基于 P-HFEs 损失函数，我们提出了具有概率犹豫模糊决策理论粗糙集（P-HFDTRSs）的 TWD。最后，为了验证我们提出的方法的有效性，我们开发了一系列对比实验并讨论了六个 UCI 数据集的决策结果。