Cone distribution functions from statistics are turned into Multi-Criteria Decision Making tools. It is demonstrated that this procedure can be considered as an upgrade of the weighted sum scalarization insofar as it absorbs a whole collection of weighted sum scalarizations at once instead of fixing a particular one in advance. As examples show, this type of scalarization--in contrast to a pure weighted sum scalarization-is also able to detect ``non-convex" parts of the Pareto frontier. Situations are characterized in which different types of rank reversal occur, and it is explained why this might even be useful for analyzing the ranking procedure. The ranking functions are then extended to sets providing unary indicators for set preferences which establishes, for the first time, the link between set optimization methods and set-based multi-objective optimization. A potential application in machine learning is outlined.

翻译：统计学中的锥分布函数被转化为多准则决策工具。研究表明，该方法可视为加权和标量化的升级，其能一次性吸收整个加权和标量化集合，而非预先固定某一特定标量化方式。示例表明，与纯加权和标量化相比，此类标量化方法还能检测帕累托前沿的“非凸”部分。本文刻画了不同类型排序反转发生的情境，并阐释了为何这对分析排序过程可能具有实际价值。随后将排序函数扩展至集合层面，为集合偏好提供一元指标，首次建立了集合优化方法与基于集合的多目标优化之间的关联。最后概述了该方法在机器学习中的潜在应用。