We propose a version of ordered weighted averaging (OWA) operators, which are robust against inputs with outliers. Outliers may heavily bias the outputs of the standard OWA. The penalty-based method proposed here comprises both outlier detection and reallocation of weights of the OWA. At the first stage, the outliers are identified based on a robust criterion that can accommodate up to half the inputs being outliers, but at the same time not removing the inputs unnecessarily. Three numerical algorithms for calculating the optimal value of this criterion are proposed. At the second stage, the OWA weights are recalculated for a subset of clean data while preserving the overall character of the weighting vector. The method is numerically tested on simulated data and exemplified on aggregating a large number of online ratings where the outliers represent biased, missing, or erroneous evaluations.

中文翻译：

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加强 OWA 算子以将数据与异常值聚合

我们提出了一种有序加权平均 (OWA) 算子的版本，它对具有异常值的输入具有鲁棒性。异常值可能会严重影响标准 OWA 的输出。这里提出的基于惩罚的方法包括异常值检测和 OWA 权重的重新分配。在第一阶段，基于稳健的标准识别异常值，该标准可以容纳多达一半的异常值输入，但同时不会不必要地移除输入。提出了三种计算该准则最优值的数值算法。在第二阶段，为干净数据的子集重新计算 OWA 权重，同时保留权重向量的整体特征。