Probabilistic linguistic term sets (PLTSs) have many applications in the field of group decision making (GDM) because it includes both linguistic evaluation and probabilistic distribution when expressing preference information. However, the difference of information credibility in PLTSs is ignored, resulting in an inaccurate representation of decision information and unreasonable probability calculation. In this paper, we first consider the credibility of the information and propose the concept of Z‐uncertain probabilistic linguistic variables (Z‐UPLVs). Subsequently, the operational rules, normalization, distance and similarity measures, and comparison method of Z‐UPLVs are introduced. Then, a probability calculation method based on credibility, an extended TOPSIS method, and some operators are proposed, which can be applied to emergency decision making in the Z‐uncertain probabilistic linguistic (Z‐UPL) environment. Finally, an emergency decision‐making case of COVID‐19 patients and comparative analysis illustrate the necessity and effectiveness of this method.

中文翻译：

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Z-不确定概率语言变量及其在治疗COVID-19患者的紧急决策中的应用

概率语言术语集（PLTS）在群体决策（GDM）领域有很多应用，因为它在表达偏好信息时既包括语言评估，也包括概率分布。然而，PLTSs中信息可信度的差异被忽略，导致决策信息表示不准确和概率计算不合理。在本文中，我们首先考虑信息的可信度，并提出 Z-不确定概率语言变量 (Z-UPLVs) 的概念。随后，介绍了Z-UPLVs的运算规则、归一化、距离和相似度度量以及比较方法。然后，提出了一种基于可信度的概率计算方法，一种扩展的TOPSIS方法，以及一些算子，可应用于 Z-不确定概率语言 (Z-UPL) 环境中的紧急决策。最后，以 COVID-19 患者的紧急决策案例和对比分析说明了该方法的必要性和有效性。