Abstract Aggregation functions have attracted much attention in recent times because of its potential use in many areas such us data fusion and decision making. In practice, most of the aggregation functions that scientists use in their studies are constructed from very simple (usually affine or polynomial) functions. However, these are distinct in nature. In this paper, we develop a systematic study of these two classes of functions from a common point of view. To do this, we introduce the class of affine aggregation functions, which cover both the aforementioned families and most of examples of aggregation functions that are used in practice, including, by its great applicability, the symmetric case. Our study allows us to characterize when a function constructed from affine or polynomial functions is, in fact, a new aggregation function. We also study when sums or products of this kind of functions are again an aggregation function.

中文翻译：

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聚合函数的仿射构造方法

摘要 聚合函数由于其在数据融合和决策制定等许多领域的潜在用途，近年来备受关注。实际上，科学家在研究中使用的大多数聚合函数都是由非常简单的（通常是仿射或多项式）函数构建的。然而，这些在本质上是不同的。在本文中，我们从一个共同的角度对这两类函数进行了系统的研究。为此，我们引入了仿射聚合函数类，它涵盖了上述家族和实践中使用的聚合函数的大多数示例，包括其极大的适用性，对称情况。我们的研究使我们能够表征由仿射函数或多项式函数构造的函数实际上何时是新的聚合函数。