The decision-maker's judgment deviates from uncertain attribute information will lead to decision risk in multiple attribute decision making (MADM), and different aggregation approaches result in different risk levels. This paper aims to study the risk levels of aggregation operators in MADM with uncertain attribute information. We use the signal detection theory to characterize the decision-maker's noisy perceptions of multiple attributes to present his/her judgment deviation. Then, we establish the aggregation models to aggregate these perceptions based on the weighted averaging (WA) and the ordered weighted averaging (OWA) operators. Furthermore, a risk measurement model of each aggregation approach is constructed to measure the risk levels of the commission risk (CR), the omission risk (OR), and the overall risk. A numerical example is used to verify the validity of the proposed model, while simulation experiments are designed to compare the risk levels of the WA and OWA operators. The results reveal that the overall risk level of the WA operator is higher than that of the OWA operator when judging the quality of the alternative with high standards; otherwise, the WA operator is lower. This finding provides a scientific reference for aggregation approach selection under uncertain information. Permanent link to reproducible Capsule: .

中文翻译：

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不确定信息下多属性决策聚合方法的风险度量

多属性决策（MADM）中，决策者的判断偏离不确定的属性信息会导致决策风险，不同的聚合方式会导致不同的风险级别。本文旨在研究属性信息不确定的MADM中聚合算子的风险水平。我们利用信号检测理论来表征决策者对多个属性的噪声感知，以呈现他/她的判断偏差。然后，我们建立聚合模型来基于加权平均（WA）和有序加权平均（OWA）算子来聚合这些感知。此外，构建了每种聚合方法的风险度量模型，以度量佣金风险（CR）、遗漏风险（OR）和总体风险的风险水平。通过数值算例验证了所提模型的有效性，同时设计了仿真实验来比较WA和OWA运营商的风险水平。结果表明，在高标准判断替代方案质量时，WA运营商的总体风险水平高于OWA运营商；否则，WA算子较低。这一发现为不确定信息下聚合方法的选择提供了科学参考。可复制胶囊的永久链接：.