Bi-Choquet Integrals based on bi-capacities are very powerful aggregation operators introduced by Grabisch and Labreuche, and they can generalize Choquet Integrals. Bi-capacities can model a lager range of preferences than capacities. However, there are few existent knowledge about constructing bi-capacities, and there lacks the practical and reasonable orness/andness definitions for bi-capacities to present an effective optimism/pessimism indicator. We present a convenient way to generate bi-capacities. As the main proposal of this study, we propose an orness/andness definition for bi-capacities. Although structurally complex in defining, with the help of one interesting proposition related to bi-Choquet Integral, its reasonability in the way of constructing further proves it can indeed serve as a perfect generalization of orness/andness for capacities.

中文翻译：

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论双容量的一些施工方法和完整性措施

基于双容量的 Bi-Choquet Integrals 是 Grabisch 和 Labreuche 引入的非常强大的聚合算子，它们可以泛化 Choquet Integrals。双容量可以模拟比容量更大的偏好范围。然而，关于构建双容量的现有知识很少，并且缺乏实用和合理的双容量定义来呈现有效的乐观/悲观指标。我们提出了一种方便的方法来生成双容量。作为本研究的主要建议，我们提出了双容量的 orness/andness 定义。尽管在定义上结构复杂，但借助与 bi-Choquet Integral 相关的一个有趣命题，