Abstract The Crescent Method is a recently proposed decision method that can consider problems involving both risk and preferences. In this work, we elaborately discuss why and how to use this interesting method in decision making. We present its advantages in accurately merging both types of decisions. However, not all preferences are suitable to use with the Crescent Method and for melting with probability information. This study systematically proposes and analyzes those subclasses of preference vectors that are suitable for the Crescent Method. Unimodal preferences are shown to be suitable for the Crescent Method, but they are not closed under convex combination. Pure crescent preferences are shown to be suitable for the Crescent Method and to have the property of convexity. The interrelations and inclusions of certain different subclasses of preference vectors along with some examples are presented in detail.

中文翻译：

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新月偏好向量的特性及其在风险和偏好决策中的效用

摘要 新月法是最近提出的一种决策方法，可以考虑涉及风险和偏好的问题。在这项工作中，我们精心讨论了为什么以及如何在决策中使用这种有趣的方法。我们展示了它在准确合并两种类型的决策方面的优势。但是，并非所有首选项都适合与 Crescent Method 一起使用并适合使用概率信息进行融合。本研究系统地提出并分析了适用于新月法的偏好向量子类。单峰偏好被证明适用于新月方法，但它们在凸组合下不是封闭的。纯新月偏好被证明适用于新月方法并具有凸性属性。