The notion of an orness measure for aggregation functions has been a relevant study subject whose history can be traced back to the early works of Dujmović in 1973. Intuitively, an orness measure quantifies the similarity of an aggregation function to the “or” function and results in an essential tool for decision engineering, field in which the choice of aggregation function is sometimes restricted to a desired value of orness (orness‐directed aggregation). In 1988, Yager presented a particular example of orness measure for ordered weighted averaging (OWA) functions and initiated a series of contributions aiming at proposing an axiomatic definition of orness measure for OWA functions. In this paper, we go much further and present an axiomatic definition of orness measure for the whole family of aggregation functions. We end by proposing two natural construction methods for an orness measure for aggregation functions. The particular examples of the (discrete) Choquet integral and uninorms are studied in detail.

中文翻译：

---

聚集功能的公理化和orness度量的构造

聚合函数的Orness度量的概念一直是相关的研究主题，其历史可以追溯到1973年Dujmović的早期著作。从直觉上讲，Orness度量量化了聚合函数与“或”函数和结果的相似性。在决策工程的基本工具中，聚合函数的选择有时会局限于orness的期望值（orness定向聚合）领域。1988年，Yager提出了用于有序加权平均（OWA）函数的Orness度量的一个特定示例，并发起了一系列旨在提出OWA函数Orness度量的公理定义的贡献。在本文中，我们走得更远，并为整个聚合函数族提供了orness度量的公理定义。最后，我们针对聚合函数的orness量度提出了两种自然的构造方法。（离散）Choquet积分和uninorms的特定示例进行了详细研究。