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今天小编为您带来精读博士论文《广义乘性偏好信息下考虑专家共识的多属性群决策方法》5.5算例分析（1）。
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Today, the editor brings the " 5.5 example analysis (1) of the intensively read PhD thesis 'A Multi-Attribute Group Decision-Making approach considering expert consensus under generalised nultiplicative preference information'".
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一、内容摘要（Content Summary）
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博士论文《广义乘性偏好信息下考虑专家共识的多属性群决策方法》的5.5算例分析（1）。
This issue of the article will introduce the 5.5 example analysis (1) from three aspects: mind mapping, in-depth reading content, and supplementary knowledge, focusing on the doctoral dissertation "Multi-attribute Group Decision-making Method Considering Expert Consensus under Generalized Multiplicative Preference Information".
二、思维导图（Mind Mapping）
三、精读内容（Detailed Reading Content）
（一）算例介绍（Case Study）
该算例假设某大学宿舍中4名学生想要选取合适的宽带网络安装套餐，以供日常学习生活使用。共有4种可选择的宽带，影响最终套餐方案选取的评估属性有套餐价格、网络速度、每月使用津贴以及售后服务质量等。具体情况如下图所示。
Introduction This case study assumes that four students in a university dormitory want to select a suitable broadband network installation package for daily study and life use. There are four broadband options to choose from, and the evaluation attributes affecting the final package selection include package price, network speed, monthly usage allowance, and after-sales service quality. The specific situation is as shown in the figure below.
该算例的计算过程分为两种，一是专家未参与一致性与共识水平改进过程，二是专家参与一致性与共识水平改进过程。
The calculation process of this case study is divided into two types: one is where experts do not participate in the consistency and consensus level improvement process, and the other is where experts participate in the consistency and consensus level improvement process.
（二）专家未参与一致性与共识水平改进过程（Experts Not Participating in the Consistency and Consensus Level Improvement Process）
专家未参与一致性与共识水平改进过程如下图所示。在第8步中，专家群体尚未达成可接受共识，于是对其进行可接受公式改进，经过7轮迭代集结得到群体直觉乘性偏好信息（IMPR）。
The process where experts do not participate in the consistency and consensus level improvement process is shown in the figure below. In step 8, the expert group has not yet reached an acceptable consensus, so an acceptable formula improvement is made, and after 7 rounds of iteration, the group's intuitive multiplicative preference information (IMPR) is obtained.
运用可视化方法（区域图）去体现原始IMPR与算法5.4得到的可接受一致与共识 IMPR的一致性与共识水平的差异，因此，结合第2章定义中的记分函数将上述 IMPR 中的直觉乘性偏好信息转化为其记分函数值形式，并绘制区域图，如图5-3与5-4所示。由图5-3与5-4可以看出，可接受一致与共识IMPR所对应的区域图中各个颜色区域要比原始IMPR中各个颜色区域表现得更加规律，此外，可接受一致与共识IMPR所对应的4个区域图更为类似，这表明可接受一致与共识IMPR具有更好的一致性与共识水平。
Using a visual method (area chart) to reflect the difference in consistency and consensus levels between the original IMPR and the acceptable consistent and consensus IMPR obtained from algorithm 5.4. Therefore, combining the scoring function defined in Chapter 2, the intuitive multiplicative preference information in the above IMPR is converted into its scoring function value form and plotted on the area chart, as shown in Figures 5-3 and 5-4. From Figures 5-3 and 5-4, it can be seen that the various colored areas in the region graphs corresponding to the acceptable consistent and consensus IMPR are more regular than those in the original IMPR. Furthermore, the four region graphs corresponding to the acceptable consistent and consensus IMPR are more similar, indicating that the acceptable consistent and consensus IMPR has better consistency and consensus levels.
（三）专家参与一致性与共识水平改进过程（Experts Participating in the Consistency and Consensus Level Improvement Process）
当专家参与一致性与共识水平改进过程，即运用算法5.5解决该多属性群决策（MAGDM）问题时，决策步骤如下图所示。该算例的专家群体的全局一致性与共识水平为未达到可接受条件。针对识别准则确定的非一致与非共识偏好信息集中的直觉乘性偏好信息，计算其与群体 IMPR和一致 IMPR 对应位置的综合直觉乘性偏好信息的大小关系，指导专家改进偏好信息。
When experts participate in the consistency and consensus level improvement process, that is, when using algorithm 5.5 to solve the Multiple Attribute Group Decision Making (MAGDM) problem, the decision steps are as shown in the figure below. The global consistency and consensus level of the expert group in this case study did not meet the acceptable conditions. For the intuitive multiplicative preference information concentrated in the non-consistent and non-consensus preference information set identified by the recognition criteria, the size relationship between the comprehensive intuitive multiplicative preference information and the group IMPR and consistent IMPR corresponding positions is calculated to guide the experts in improving the preference information.
同理，运用可视化方法绘制算法5.5得到的可接受一致与共识IMPR的区域图，如下图所示。可以看出，可接受一致与共识IMPR相比原始IMPR具有更好的一致性与共识水平。
Similarly, using a visual method to draw the region graph of the acceptable consistent and consensus IMPR obtained from algorithm 5.5, as shown in the figure below. It can be seen that the acceptable consistent and consensus IMPR has better consistency and consensus levels compared to the original IMPR.
四、知识补充——区域图（Additional Knowledge —— Area Chart）
区域图是一种折线图，其中线和轴之间的区域用颜色标记为阴影。这些图表通常用于表示一段时间内的累计合计，是显示堆叠线条的便携方式。Matlab中绘制区域图的代码示例如下图所示。
An area chart is a type of line chart where the area between the lines and the axes is shaded with colors. These charts are typically used to show cumulative totals over time and provide a convenient way to display stacked lines. An example of code for drawing an area chart in Matlab is shown in the figure below.
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参考资料：ChatGPT、百度百科
参考文献：
王睿. 广义乘性偏好信息下考虑专家共识的多属性群决策方法 [D]. 四川: 西南交通大学, 2022.
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