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Today, Xiaobian brings you an intensive reading of the doctoral dissertation "Multi-attribute Group Decision Making Method Considering Expert Consensus under Generalized Multiplicative Preference Information" 5.5 Case Study (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）
In this issue, we will introduce the 5.5 case analysis of the doctoral dissertation "Multi-attribute Group Decision Making Method Considering Expert Consensus under Generalized Multiplicative Preference Information" from three aspects: mind map, intensive reading content, and knowledge supplementation (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）
This example assumes that four students in a university dormitory want to choose a suitable broadband network installation package for their daily study and life. There are 4 types of broadband to choose from, and the evaluation attributes that affect the final package plan selection are package price, network speed, monthly usage allowance, and after-sales service quality. The details are shown in the figure below.
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.
The calculation process of this study is divided into two types, one is that the experts do not participate in the process of improving the consistency and consensus level, and the other is that the experts participate in the process of improving the consistency and consensus level.
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）
Experts are not involved in the process of improving the level of consistency and consensus, as shown in the figure below. In the eighth step, the expert community has not yet reached an acceptable consensus, so the acceptability formula is improved, and the group intuitive multiplicative preference information (IMPR) is obtained after 7 rounds of iterative assembly.
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.
The visualization method (area map) is used to reflect the difference between the consistency and consensus level of the acceptable consensus and consensus IMPR obtained by the original IMPR and algorithm 5.4, therefore, combined with the scoring function in the definition of Chapter 2, the intuitive multiplicative preference information in the above IMPR is converted into the form of the score function value, and the area plot is drawn, as shown in Figs. 5-3 and 5-4. As can be seen from Figures 5-3 and 5-4, the color regions in the region diagram corresponding to the acceptable agreement and consensus IMPR are more regular than those in the original IMPR, and the four regions corresponding to the acceptable agreement and consensus IMPR are more similar, which indicates that the acceptable consensus and consensus IMPR have better consistency and consensus levels.
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）
When experts participate in the process of improving the level of consensus and consensus, that is, using algorithm 5.5 to solve the multi-attribute group decision making (MAGDM) problem, the decision-making steps are shown in the figure below. The global consensus and consensus level of the expert group in this study is that the acceptable condition is not met. Aiming at the intuitionistic multiplicative preference information in the non-congruent and non-consensus preference information set determined by the identification criteria, the magnitude relationship between the comprehensive intuitionistic multiplicative preference information and the corresponding positions of the population IMPR and the consistent IMPR is calculated, and the experts are guided to improve the preference information.
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.
In the same way, the visual method is used to draw the region diagram of acceptable agreement and consensus IMPR obtained by algorithm 5.5, as shown in the following figure. It can be seen that the acceptable consensus and consensus IMPR have a better level of consensus and consensus than the original IMPR.
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）
An area chart is a type of line chart in which the area between the lines and axes is color-coded as a shade. These charts are often used to represent cumulative totals over time and are a portable way to display stacked lines. The following is an example of the code for drawing an area diagram in MATLAB.
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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References: ChatGPT, Baidu Encyclopedia
Bibliography:
WANG Rui. Multi-attribute group decision-making method considering expert consensus under generalized multiplicative preference information[D]. Sichuan: Southwest Jiaotong University, 2022.
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