Building green airports can be regarded as among the most promising routes to sustainable development of ecosystems and human health. This study aims at addressing the problem of green airport plan selection under an uncertain context by developing an uncertain multiattribute group decision making (MAGDM) model. In the proposed model, the assessment information is characterized in the form of a proportional hesitant 2-tuple linguistic term set (PH2TLTS), which incorporates in binary form linguistic information that can accurately quantify subjective assessment information provided under uncertainty. The weights of assessment attributes of green airport plans are obtained automatically through a nonlinear programming model, which enhances the robustness of the decision-making method. Subsequently, on the basis of PH2TLTSs, three distance measures are proposed: the proportional hesitant 2-tuple linguistic Jaccard distance (PH2TLJD), the supplementary proportional hesitant 2-tuple linguistic normalized Minkowski distance (SPH2TLNMD) and the cluster-based proportional hesitant 2-tuple linguistic normalized Minkowski distance (CBPH2TLNMD). The TOPSIS-based comparison method proposed here can better determine the priorities of PH2TLTSs. The ranking and selection of green airport plans are derived using the PH2TL-VIKOR model. Finally, a case study accompanied by sensitivity and comparative analyses is performed to verify the rationality and feasibility of the proposed model.

中文翻译：

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比例犹豫二元组语言距离测量与扩展 VIKOR 方法：绿色机场规划评估与选择案例研究

建设绿色机场被认为是生态系统可持续发展和人类健康最有希望的途径之一。本研究旨在通过开发一个不确定的多属性群决策（MAGDM）模型来解决不确定环境下的绿色机场规划选择问题。在所提出的模型中，评估信息以比例犹豫二元组语言术语集（PH2TLTS）的形式表征，它以二进制形式包含语言信息，可以准确量化在不确定性下提供的主观评估信息。通过非线性规划模型自动获得绿色机场规划评估属性的权重，增强了决策方法的鲁棒性。随后，在 PH2TLTS 的基础上，提出了三种距离度量：比例犹豫二元组语言 Jaccard 距离 (PH2TLJD)、补充比例犹豫二元语言归一化 Minkowski 距离 (SPH2TLNMD) 和基于聚类的比例犹豫二元语言归一化 Minkowski 距离 (CBPH2TLNMD) . 这里提出的基于 TOPSIS 的比较方法可以更好地确定 PH2TLTS 的优先级。使用 PH2TL-VIKOR 模型得出绿色机场规划的排名和选择。最后，通过案例研究，结合敏感性分析和对比分析，验证了所提模型的合理性和可行性。补充比例犹豫二元组语言归一化 Minkowski 距离 (SPH2TLNMD) 和基于集群的比例犹豫二元语言归一化 Minkowski 距离 (CBPH2TLNMD)。这里提出的基于 TOPSIS 的比较方法可以更好地确定 PH2TLTS 的优先级。使用 PH2TL-VIKOR 模型得出绿色机场规划的排名和选择。最后，通过案例研究，结合敏感性分析和对比分析，验证了所提模型的合理性和可行性。补充比例犹豫二元组语言归一化 Minkowski 距离 (SPH2TLNMD) 和基于集群的比例犹豫二元语言归一化 Minkowski 距离 (CBPH2TLNMD)。这里提出的基于 TOPSIS 的比较方法可以更好地确定 PH2TLTS 的优先级。使用 PH2TL-VIKOR 模型得出绿色机场规划的排名和选择。最后，通过案例研究，结合敏感性分析和对比分析，验证了所提模型的合理性和可行性。