The data are not always real numbers due to the complexity and uncertainty of the real-world decision environment. This requires us to use probability-based expressions to describe the complex decision-making data in reality. In order to understand the probability-based decision-making information more comprehensively, this paper reviews and summarizes the current development of probability-based decision-making information. First, the number and the distribution of publications related to the probability-based decision-making information are analyzed. Then, based on presenting literature related to different concepts, all the existing different concepts are reviewed and discussed. Considering different forms of decision-making information, this paper summarizes decision-making methods from two aspects: the decision-making methods based on decision matrix and the decision-making methods based on preference information. We also summarize the existing literature from the perspective of application. In addition, based on current developments and the discussions above, some challenges concerning probability-based expressions are listed, which can be regarded as future research directions.

由于现实世界决策环境的复杂性和不确定性，数据并不总是实数。这就要求我们使用基于概率的表达式来描述现实中复杂的决策数据。为了更全面地了解概率决策信息，本文对概率决策信息的发展现状进行了回顾和总结。首先，分析了与基于概率的决策信息相关的出版物的数量和分布。然后，在介绍与不同概念相关的文献的基础上，回顾和讨论所有现有的不同概念。考虑到不同形式的决策信息，本文从两个方面总结了决策方法：基于决策矩阵的决策方法和基于偏好信息的决策方法。我们还从应用的角度总结了现有的文献。此外，基于目前的发展和上述讨论，列出了基于概率表达式的一些挑战，可以作为未来的研究方向。