Loss functions, commonly believed to be the cost of cognitive computing, are a key element in decision-making, and three-way decisions can be regarded as a cognitive computing method that seeks to minimize the overall risks involved in the decision-making process. Recently, many studies on loss functions have been conducted based on fuzzy sets, intuitionistic fuzzy sets, and interval intuitionistic fuzzy sets. However, most of these studies draw conclusions based on two descriptions, which may fail to capture the whole picture of decision-making. In this paper, in order to improve the accuracy of decision-making, we propose loss functions based on three descriptions, adding a hesitation description to the Pythagorean fuzzy environment. Then, we redefine the expected loss functions, which allow people to make a decision with more uncertainty. Subsequently, on the basis of the Bayesian minimum risk decision theory, four strategies for dealing with expected losses are proposed, and three-way decision models are established. Finally, group decision models are discussed. Three-way decision models of real value loss functions and Pythagorean fuzzy loss functions based on three descriptions are proposed, and data analyses of different parameters show the feasibility of the three-way decision models.

损失函数，通常被认为是认知计算的成本，是决策的关键要素，三向决策可以看作是一种寻求最小化决策过程中整体风险的认知计算方法。近年来，基于模糊集、直觉模糊集和区间直觉模糊集对损失函数进行了许多研究。然而，这些研究大多基于两种描述得出结论，这可能无法捕捉到决策的全貌。在本文中，为了提高决策的准确性，我们提出了基于三种描述的损失函数，在勾股模糊环境中加入了犹豫描述。然后，我们重新定义了预期损失函数，这使人们可以做出具有更多不确定性的决策。随后，在贝叶斯最小风险决策理论的基础上，提出了四种应对预期损失的策略，并建立了三向决策模型。最后，讨论了群决策模型。提出了基于三种描述的实值损失函数和勾股模糊损失函数的三路决策模型，对不同参数的数据分析表明了三路决策模型的可行性。