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今天小編為您帶來精讀博士論文《廣義乘性偏好資訊下考慮專家共識的多屬性群決策方法》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）
本期推文将從思維導圖、精讀内容、知識補充三個方面介紹精讀博士論文《廣義乘性偏好資訊下考慮專家共識的多屬性群決策方法》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、思維導圖（Mind Mapping）
三、精讀内容（Detailed Reading Content）
（一）算例介紹（Case Study）
該算例假設某大學宿舍中4名學生想要選取合适的寬帶網絡安裝套餐，以供日常學習生活使用。共有4種可選擇的寬帶，影響最終套餐方案選取的評估屬性有套餐價格、網絡速度、每月使用津貼以及售後服務品質等。具體情況如下圖所示。
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.
該算例的計算過程分為兩種，一是專家未參與一緻性與共識水準改進過程，二是專家參與一緻性與共識水準改進過程。
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）專家未參與一緻性與共識水準改進過程（Experts Not Participating in the Consistency and Consensus Level Improvement Process）
專家未參與一緻性與共識水準改進過程如下圖所示。在第8步中，專家群體尚未達成可接受共識，于是對其進行可接受公式改進，經過7輪疊代集結得到群體直覺乘性偏好資訊（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.
運用可視化方法（區域圖）去展現原始IMPR與算法5.4得到的可接受一緻與共識 IMPR的一緻性與共識水準的差異，是以，結合第2章定義中的記分函數将上述 IMPR 中的直覺乘性偏好資訊轉化為其記分函數值形式，并繪制區域圖，如圖5-3與5-4所示。由圖5-3與5-4可以看出，可接受一緻與共識IMPR所對應的區域圖中各個顔色區域要比原始IMPR中各個顔色區域表現得更加規律，此外，可接受一緻與共識IMPR所對應的4個區域圖更為類似，這表明可接受一緻與共識IMPR具有更好的一緻性與共識水準。
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）專家參與一緻性與共識水準改進過程（Experts Participating in the Consistency and Consensus Level Improvement Process）
當專家參與一緻性與共識水準改進過程，即運用算法5.5解決該多屬性群決策（MAGDM）問題時，決策步驟如下圖所示。該算例的專家群體的全局一緻性與共識水準為未達到可接受條件。針對識别準則确定的非一緻與非共識偏好資訊集中的直覺乘性偏好資訊，計算其與群體 IMPR和一緻 IMPR 對應位置的綜合直覺乘性偏好資訊的大小關系，指導專家改進偏好資訊。
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，運用可視化方法繪制算法5.5得到的可接受一緻與共識IMPR的區域圖，如下圖所示。可以看出，可接受一緻與共識IMPR相比原始IMPR具有更好的一緻性與共識水準。
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、知識補充——區域圖（Additional Knowledge —— Area Chart）
區域圖是一種折線圖，其中線和軸之間的區域用顔色标記為陰影。這些圖表通常用于表示一段時間内的累計合計，是顯示堆疊線條的便攜方式。Matlab中繪制區域圖的代碼示例如下圖所示。
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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參考資料：ChatGPT、百度百科
參考文獻：
王睿. 廣義乘性偏好資訊下考慮專家共識的多屬性群決策方法 [D]. 四川: 西南交通大學, 2022.
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