Ordered weighted averaging (OWA) operators, a family of aggregation functions, are widely used in human decision-making schemes to aggregate data inputs of a decision maker's choosing through a process known as OWA aggregation. The weight allocation mechanism of OWA aggregation employs the principle of linear ordering to order data inputs after the input variables have been rearranged. Thus, OWA operators generally cannot be used to aggregate a collection of $n$ inputs obtained from any given convex partially ordered set (poset). This poses a problem since data inputs are often obtained from various convex posets in the real world. To address this problem, this paper proposes methods that practitioners can use in real-world applications to aggregate a collection of $n$ inputs from any given convex poset. The paper also analyzes properties related to the proposed methods, such as monotonicity and weighted OWA aggregation on convex posets.

中文翻译：

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Convex Poset 上的有序加权平均聚合

有序加权平均 (OWA) 算子是一组聚合函数，广泛用于人类决策方案，通过称为 OWA 聚合的过程聚合决策者选择的数据输入。OWA 聚合的权重分配机制采用线性排序原则，在输入变量重新排列后对数据输入进行排序。因此，OWA 运算符通常不能用于聚合一组$n$从任何给定的凸偏序集（poset）获得的输入。这带来了一个问题，因为数据输入通常是从现实世界中的各种凸偏集获得的。为了解决这个问题，本文提出了一些方法，从业者可以在现实世界的应用程序中使用这些方法来聚合一组$n$来自任何给定凸偏集的输入。该论文还分析了与所提出方法相关的属性，例如凸偏集上的单调性和加权 OWA 聚合。