摘要：本期推文将从思维导图、精读内容、知识补充三个方面介绍精读期刊论文《Multi-criteria decision support and uncertainty handling, propagation and visualisation for emerg
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今天小编为您带来“越览（146）——精读期刊论文
《Multi-criteria decision support
and uncertainty handling, propagation and
visualisation for emergency and
remediation management》的
3 不确定性处理、传播和可视化（2）”。
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Today, the editor brings the
＂Yue Lan (146)：Intensive reading of the journal article
＇Multi-criteria decision support
and uncertainty handling, propagation and
visualisation for emergency and
remediation management’
3 Uncertainty handling, propagation, and visualization(2)".
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一、内容摘要（Summary of Content）
本期推文将从思维导图、精读内容、知识补充三个方面介绍精读期刊论文《Multi-criteria decision support and uncertainty handling, propagation and visualisation for emergency and remediation management》的3 不确定性处理、传播和可视化（2）。
This issue of tweets will introduce the 3 Uncertainty handling, propagation, and visualization (2) of the intensive reading journal article "Multi-criteria decision support and uncertainty handling, propagation and visualisation for emergency and remediation management" from three aspects: mind map, intensive reading content, and knowledge supplement.
二、思维导图（Mind Mapping）
三、精读内容（Intensive reading content）
（一）不确定性的建模和传播（Modeling and propagation of uncertainty）
由于源项分析系统（ASY）预测存在不确定性，因此需要对建模过程中的不确定性进行评估。源项和风向是两个主要变量，其中源项服从对数正态分布，表示其数量级上的偏差在增加和减少方向上具有相同的概率；风向服从正态分布，标准差为30°。采用蒙特卡洛方法，可以将这些不确定性从ASY依次传递至传输分析系统（CSY）和效应分析系统（ESY）。
Due to the uncertainty in the predictions of the source analysis system (ASY), it is necessary to evaluate the uncertainty in the modeling process. The source term and wind direction are the two main variables, where the source term follows a lognormal distribution, indicating that deviations in its magnitude have the same probability in the increasing and decreasing directions; the wind direction follows a normal distribution with a standard deviation of 30°. Using the Monte Carlo method, these uncertainties can be transferred from the ASY to the transmission analysis system (CSY) and the effects analysis system (ESY) in turn.
（二）Web-HIPRE中的不确定性处理和可视化（ Uncertainty handling and visualisation in Web-HIPRE）
本部分采用蒙特卡洛方法传播不确定性，在ASY启动前，根据源项和风向的概率分布生成多个样本，并将其作为输入进行多次并行运行，从而得到多个应对措施结果。Web-HIPRE中的决策分析基于多个决策表，每个表对应一个样本（即一种情景），并同时进行评估。
This part adopts the Monte Carlo method to propagate uncertainty. Before the ASY is started, multiple samples are generated according to the probability distribution of source terms and wind directions, and they are used as input for multiple parallel runs to obtain multiple response measures. The decision analysis in Web-HIPRE is based on multiple decision tables, each of which corresponds to a sample (i.e., a scenario) and is evaluated simultaneously.
为避免信息过载，结果可视化仅展示最可能情景以及整体得分的5%和95%分位数对应的情景，分别代表最差和最佳情景。这种方式能够传达决策结果的不确定范围，例如某方案得分低于95%分位数情景的概率至少为95%。
To avoid information overload, the result visualization only shows the most likely scenario and the scenarios corresponding to the 5% and 95% percentiles of the overall score, representing the worst and best scenarios, respectively. This approach can convey the uncertainty range of the decision results, for example, the probability that a certain solution scores below the 95% percentile scenario is at least 95%.
图2展示了在多准则决策分析中对“接受度”这一准则权重的扩展敏感性分析结果。该图的核心目的是同时呈现输入数据不确定性和模型参数不确定性对决策结果的影响。分析的重点是识别当前设定下表现最好的方案，并评估其在不同情景下的稳健性。
Figure 2 shows the results of an extended sensitivity analysis of the weight of the criterion "acceptance" in multi-criteria decision-making analysis. The core purpose of this figure is to simultaneously present the impact of input data uncertainty and model parameter uncertainty on decision results. The focus of the analysis is to identify the best performing solution under the current settings and evaluate its robustness under different scenarios.
具体而言，图中针对当前“接受度”权重设定下总得分最高的方案，展示了三个情景对应的绩效得分：
Specifically, the figure shows the performance scores of the three scenarios for the solution with the highest total score under the current "acceptance" weight setting:
1.最可能情景：对应于源项和风向变量的概率分布中最常出现的样本，代表方案在典型条件下的表现。
1. Most likely scenario: corresponds to the most frequently occurring sample in the probability distribution of the source term and wind direction variables, representing the performance of the scheme under typical conditions.
2.最差情景（5%分位数）：表示该方案在95%的模拟情景中，其得分都优于该情景，代表极端不利条件下的结果。
2. Worst Scenario (5% quantile): This means that the solution scores better than this scenario in 95% of the simulated scenarios, representing the result under extremely unfavorable conditions.
3.最佳情景（95%分位数）：表示该方案在95%的模拟情景中，其得分都低于该情景，代表极端有利条件下的结果。
3. Best scenario (95% quantile): This means that the solution scores lower than this scenario in 95% of the simulated scenarios, representing the result under extremely favorable conditions.
通过这种方式，图2不仅展示了某一权重设定下某方案的“平均”表现，还揭示了其在不确定条件下可能出现的波动区间。决策者可以据此评估方案的稳健性，即在面对输入参数波动和不确定性时，该方案能否仍保持较优表现。
In this way, Figure 2 not only shows the "average" performance of a solution under a certain weight setting, but also reveals its possible fluctuation range under uncertain conditions. Decision makers can use this to evaluate the robustness of the solution, that is, whether the solution can still maintain better performance in the face of input parameter fluctuations and uncertainties.
四、知识补充（Knowledge supplement）
扩展敏感性分析是在传统敏感性分析基础上发展起来的一种方法，旨在同时考虑模型输入的不确定性与模型参数（特别是偏好权重）的变化对决策结果的影响。它广泛应用于多准则决策分析、风险评估、环境建模等复杂系统中。
Extended sensitivity analysis is a method developed on the basis of traditional sensitivity analysis, which aims to simultaneously consider the impact of the uncertainty of model input and the change of model parameters (especially preference weights) on decision results. It is widely used in complex systems such as multi-criteria decision analysis, risk assessment, and environmental modeling.
传统敏感性分析的核心目标是考察模型参数变化（如准则权重）对输出结果的影响，其假设前提通常是输入数据为确定性值。在MCDA中，它常用于分析当某一权重值上下波动时，最优方案是否发生变化，目的是检验决策的稳定性。
The core goal of traditional sensitivity analysis is to examine the impact of model parameter changes (such as criterion weights) on the output results, and its assumption is usually that the input data is a deterministic value. In MCDA, it is often used to analyze whether the optimal solution changes when a certain weight value fluctuates up and down, in order to test the stability of the decision.
扩展敏感性分析在传统方法之上进行了两方面的拓展：
Extended sensitivity analysis extends the traditional method in two aspects:
1. 输入数据存在不确定性（There is uncertainty in the input data）
例如，模型输入可能是概率分布而非单一值（如源项强度、风向、污染物浓度等）。这些不确定性通过蒙特卡洛模拟等手段传播至输出结果。
For example, model inputs may be probability distributions rather than single values (e.g. source intensity, wind direction, pollutant concentration, etc.) These uncertainties are propagated to the outputs through Monte Carlo simulations and other means.
2. 模型参数的变动（Changes in model parameters）
不仅考虑单一权重的变化，也考虑多个准则权重组合的变动。甚至可以考虑权重的不确定性（即将权重建模为分布）。
Not only the change of a single weight is considered, but also the change of the combination of weights of multiple criteria. Even the uncertainty of the weight can be considered (i.e. the weight can be modeled as a distribution).
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翻译：谷歌翻译
参考资料：百度百科、Chat GPT
参考文献：Jutta Geldermann, Valentin Bertsch, Otto Rentz. Multi-criteria decision support and uncertainty handling, propagation and visualisation for emergency and remediation management [J]. Operations Research, 2006, 1(1): 755-760.
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来源：LearningYard学苑
