The use of the Choquet integral in data fusion processes allows for the effective modelling of interactions and dependencies between data features or criteria. Its application requires identification of the defining capacity (also known as fuzzy measure) values. The main limiting factor is the complexity of the underlying parameter learning problem, which grows exponentially in the number of variables. However, in practice we may have expert knowledge regarding which of the subsets of criteria interact with each other, and which groups are independent. In this paper we study hierarchical aggregation processes, architecturally similar to feed-forward neural networks, but which allow for the simplification of the fitting problem both in terms of the number of variables and monotonicity constraints. We note that the Möbius representation lets us identify a number of relationships between the overall fuzzy measure and the data pipeline structure. Included in our findings are simplified fuzzy measures that generalise both k-intolerant and k-interactive capacities.

在数据融合过程中使用 Choquet 积分可以对数据特征或标准之间的交互和依赖关系进行有效建模。它的应用需要识别定义容量（也称为模糊测量）值。主要限制因素是基础参数学习问题的复杂性，其变量数量呈指数增长。然而，在实践中，我们可能拥有关于哪些标准子集相互交互以及哪些组是独立的专家知识。在本文中，我们研究了分层聚合过程，在架构上类似于前馈神经网络，但它允许在变量数量和单调性约束方面简化拟合问题。我们注意到，莫比乌斯表示使我们能够识别整体模糊度量和数据管道结构之间的许多关系。我们的研究结果中包括简化的模糊测量，它概括了两者k - 不容忍和k - 交互能力。