This paper presents a novel approach to the weighted aggregation and to determination of weights in an aggregation procedure. In our study, we introduce the concept of a weighted aggregation system that consists of two components: (1) a weighting transformation and (2) an aggregation operator, both induced by a common generator function. We provide the necessary and sufficient condition for the form of a generator function-based weighted aggregation system. We show that the weighted quasi-arithmetic means on the non-negative extended real line are none other than the aggregation functions induced by weighted aggregation systems, i.e., these means are compositions of an $n$-ary aggregation operator and $n$ weighting transformations ($n\in \mathbb{N}$, $n\ge 1$). Next, using weighted quasi-arithmetic means on the unit interval, we introduce a new, expectation level-based weight determination method and a scoring procedure. In this method, the decision-maker’s expectation levels for the input variables are directly transformed into weights by making use of the generator function of a weighted quasi-arithmetic mean. We utilize this mean as a scoring function to evaluate the decision alternatives. Lastly, by the means of illustrative numerical examples, we present a novel decision model, in which the expectation levels can be even intervals, i.e., the weights are also intervals. Finally, we get an interval-valued score for each alternative.

本文提出了一种新的加权聚合方法以及在聚合过程中确定权重的方法。在我们的研究中，我们介绍了加权聚合系统的概念，该系统由两个组件组成：(1) 加权变换和 (2) 聚合算子，两者均由通用生成器函数诱导。我们为基于生成函数的加权聚合系统的形式提供了必要和充分条件。我们证明了非负扩展实线上的加权拟算术均值正是由加权聚合系统引起的聚合函数，即这些均值是$n$-ary 聚合运算符和 $n$ 加权变换 ($n\in \mathbb{ñ}$, $n\ge 1$）。接下来，在单位区间上使用加权拟算术均值，我们介绍了一种新的、基于期望水平的权重确定方法和评分程序。该方法利用加权准算术均值的生成函数，将决策者对输入变量的期望值直接转化为权重。我们利用这个平均值作为评分函数来评估决策选择。最后，通过说明性的数值例子，我们提出了一种新颖的决策模型，其中期望水平可以是偶数区间，即权重也是区间。最后，我们得到每个备选方案的区间值分数。