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.