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Zhe Xue (28): intensive reading of doctoral dissertation
Research on Multi-attribute Group Decision Making Method Based on Probabilistic Language Termset Theory and Its Application
Multi-attribute group decision-making based on probabilistic linguistic information
Models and their applications (2)".
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" Zhexue (28): Intensive reading of doctoral dissertation
"Multi-attribute group decision-making method based on probabilistic language term set theory and its application research"
Multi-attribute group decision-making based on probabilistic language information
Model and its application (2)"
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In this issue, we will introduce the multi-attribute group decision-making model based on probabilistic language information and its application in the doctoral dissertation "Multi-attribute Group Decision-making Method and Application Research Based on Probabilistic Language Termset Theory" from three aspects: mind map, intensive reading content, and knowledge supplement.
In this tweet, I will introduce the multi-attribute group decision-making model based on probabilistic linguistic information and its application of the doctoral dissertation "Multi-attribute group decision-making method based on probabilistic linguistic term set theory and itsapplication research" from the three aspects of the mind map, the content of the intensive reading, and the knowledge supplement.
一、思维导图（Mind Map）
二、精读内容（Intensive reading content）
(1)基于 EDAS 方法的概率语言多属性群决策模型(Probabilistic linguistic multi-attribute group decision-making model based on EDAS method)
1.具体步骤(Specific steps)
Firstly, the linguistic information is converted into probabilistic linguistic representations for quantitative analysis and decision-making. Then, the data in the linguistic information matrix are normalized for subsequent analysis and comparison.
First, the language information is converted into probabilistic language representation for quantitative analysis and decision-making. Then, the data in the language information matrix is standardized for subsequent analysis and comparison.
The process of using the entropy weight method to determine the weights of each attribute in a multi-attribute decision problem. The entropy weight method is a method to objectively calculate the weight of indicators based on the concept of entropy in information theory, and its core idea is to determine the weight of each index according to the degree of variation. By assessing the degree of variation of each attribute to determine its importance, it provides an objective and scientific basis for decision-making.
The process of using the entropy weight method to determine the weight of each attribute in a multi-attribute decision-making problem. The entropy weight method is a method that objectively calculates the weight of indicators based on the concept of entropy in information theory. Its core idea is to determine the weight of each indicator according to the degree of variation of each indicator. By evaluating the degree of variation of each attribute to determine its importance, it provides an objective and scientific basis for decision-making.
All probabilistic language values under each attribute are averaged to evaluate the average performance of each scenario under that attribute. According to the different characteristics of the attributes (benefit type or cost type), different calculation methods are used to obtain the forward distance matrix and the negative distance matrix of the probability language, so as to further evaluate the relative advantages and disadvantages between the schemes.
All probability language values under each attribute are averaged to evaluate the average performance of each solution under that attribute. According to the different characteristics of the attribute (benefit type or cost type), different calculation methods are used to obtain the probability language positive distance matrix and negative distance matrix to further evaluate the relative advantages and disadvantages of each solution.
The Probabilistic Language Forward Score (PLSP) and Probabilistic Language Negative Score (PLSN) of each scheme are obtained by calculating the weighted sum of the Probabilistic Language Forward Distance Matrix (PLPDA) and the Probabilistic Language Negative Distance Matrix (PLNDA). Next, the PLSP and PLSN of each protocol obtained were normalized to eliminate dimensional differences and to obtain standardized PLSP (PLNSP) and standardized PLSN (PLNSN). The resulting PLNSP and PLNSN were arithmetic averaged to obtain the Probabilistic Language Assessment Score (PLAS) for each scheme and ranked.
The probabilistic linguistic positive score (PLSP) and probabilistic linguistic negative score (PLSN) of each solution are obtained by calculating the weighted sum of the probabilistic linguistic positive distance matrix (PLPDA) and the probabilistic linguistic negative distance matrix (PLNDA). Then, the PLSP and PLSN of each solution are standardized to eliminate the dimensional difference and obtain the standardized PLSP (PLNSP) and standardized PLSN (PLNSN). Finally, the PLNSP and PLNSN are arithmetic averaged to obtain the probabilistic linguistic assessment score (PLAS) of each solution and sorted.
2. 算例应用(Application examples)
A home appliance manufacturing enterprise in Chengdu needs to purchase a batch of raw materials and hopes to select the best green supplier from the candidate suppliers. After an initial screening, the remaining 5 candidate suppliers need to be further evaluated. Four experts were invited to evaluate the supplier from four aspects, including: Supply capacity, service level, purchase cost (cost-based index) and enterprise environment (benefit-based index), and finally A1 is the optimal solution.
A household appliance manufacturer in Chengdu needs to purchase a batch of raw materials and hopes to select the best green supplier from the candidate suppliers. After preliminary screening, there are 5 candidate suppliers left for further evaluation. Four experts were invited to evaluate the suppliers from four aspects, including supply capacity, service level, purchase cost (cost-based indicator) and corporate environment (benefit-based indicator). Finally, A1 is the best solution.
(2) 基于 MABAC 方法的概率语言多属性群决策模型(Probabilistic Linguistic Multi-attribute Group Decision Making Model Based on MABAC Method)
1.具体步骤(Specific steps)
Firstly, the attribute value of the cost-type indicator is converted into the attribute value of the corresponding benefit-type indicator. Then, a probabilistic language decision matrix Y is constructed, which is a matrix of n rows and n columns of m, and each element in the matrix, PL(g(P)) represents the corresponding Φ probabilistic language information under a certain eigenvalue g(P), where the value range of Φ is 1 to #PL(P), and #PL(P) represents the total number of possible probabilistic linguistic information under g(P). Next, the probabilistic language decision matrix is standardized, and a new standardized probabilistic language decision matrix Y' is obtained. During the normalization process, each element is divided by the average of the column in which it is located to ensure that all elements are compared on the same scale.
First, the attribute values of the cost-type indicators are converted into the attribute values of the corresponding benefit-type indicators. Then, a probabilistic language decision matrix Y is constructed, which is a matrix with m rows and n columns. Each element PL(g(P)) in the matrix represents the Φth probabilistic language information corresponding to a certain eigenvalue g(P), where the value range of Φ is 1 to #PL(P), and #PL(P) represents the total number of possible probabilistic language information under g(P). Next, this probabilistic language decision matrix is standardized to obtain a new standardized probabilistic language decision matrix Y'. During the standardization process, each element is divided by the average value of its column to ensure that all elements are compared on the same scale.
First, we need to calculate the probabilistic linguistic correlation coefficients (PLCCs) between each of the two attributes, and from these correlation coefficients, we can construct a Probabilistic Linguistic Correlation Coefficients Matrix (PLCCM), in which the elements in this matrix represent the strength of the correlation between the pairs of attributes. Next, we need to calculate the probabilistic language standard deviation (PLSD) for each attribute, which is a measure of how discrete the distribution of data is, and here it helps us judge how much each attribute changes in different situations. With the correlation coefficient and standard deviation, we can calculate the objective weight of each attribute based on these values. Finally, we need to combine the objective weights calculated above with the subjective weights given by the experts to get the combined weights of each attribute.
First, we need to calculate the probabilistic linguistic correlation coefficient (PLCC) between every two attributes. Through these correlation coefficients, we can construct a probabilistic linguistic correlation coefficient matrix (PLCCM). The elements in this matrix represent the strength of correlation between each attribute pair. Next, we need to calculate the probabilistic linguistic standard deviation (PLSD) of each attribute. The standard deviation is an indicator of the degree of dispersion of data distribution. Here it helps us judge the degree of change of each attribute under different circumstances. After we have the correlation coefficient and standard deviation, we can calculate the objective weight of each attribute based on these values. Finally, we need to combine the objective weight calculated above with the subjective weight given by the expert to get the combined weight of each attribute.
Calculate the probabilistic language-weighted Hemming distance between each scenario and the PLBAA in the probabilistic language boundary approximation region. When PLHD=0, it means that scheme A is on the boundary of PLBAA in the probabilistic language boundary approximation region. When PLHD>0, it means that scheme A is located in the upper boundary-approximation region PLBAA*, which is closer to the probabilistic language positive ideal scheme PLPIS. When PLHD<0, it means that scheme A is located in the lower boundary approximation region PLBAA, which is closer to the probability language negative ideal scheme PLNIS.
Calculate the probability language weighted Hamming distance between each solution and the probability language boundary approximation area PLBAA. When PLHD=0, it means that solution A is on the boundary of the probability language boundary approximation area PLBAA. When PLHD>0, it means that solution A is located in the upper boundary approximation area PLBAA*, closer to the probability language positive ideal solution PLPIS. When PLHD<0, it means that solution A is located in the lower boundary approximation area PLBAA, closer to the probability language negative ideal solution PNLIS.
Finally, all the alternatives are ranked and compared according to the relationship between the probabilistic language score and the size of PLSV, and the scheme corresponding to the maximum value is the optimal scheme.
Finally, all alternative plans are sorted and compared according to the probability language score value PLSV, and the plan corresponding to the maximum value is the optimal plan.
2. 算例应用(Application of calculation examples)
In order to improve network security, an enterprise in Chengdu organized 4 experts to evaluate 5 qualified network security service providers, covering equipment performance, maintenance difficulty (cost-based indicators), evaluation capabilities and emergency support capabilities (all benefit-based indicators), and using language information scales (very poor to very good) for scoring, in order to select the most suitable partner. Finally, according to the above steps, A4 is the optimal scheme.
In order to improve network security, a company in Chengdu organized four experts to evaluate five qualified network security service providers. The evaluation covered equipment performance, maintenance difficulty (cost-based indicators), evaluation capabilities, and emergency support capabilities (both benefit-based indicators). The language information scale (extremely poor to very good) was used for scoring in order to select the most suitable partner. Finally, according to the above steps, A4 was found to be the best solution.
(3)基于前景理论和 TODIM 方法的概率语言多属性群决策模型(Probabilistic linguistic multi-attribute group decision-making model based on prospect theory and TODIM method)
1.具体步骤(Specific steps)
The attribute values of the cost-based indicators are converted into the attribute values of the corresponding benefit-oriented indicators, and then the initial linguistic information matrix is transformed into a probabilistic linguistic decision matrix, in which each element, PL(P), represents the set of probabilistic linguistic information under specific conditions. Then, the probabilistic language decision matrix is standardized to obtain a standardized probabilistic language decision matrix, and its elements reflect the standardized probabilistic language information.
The attribute values of the cost-type indicators are converted into the attribute values of the corresponding benefit-type indicators, and then the initial language information matrix is converted into a probabilistic language decision matrix, in which each element PL(P) represents a set of probabilistic language information under specific conditions. After that, the probabilistic language decision matrix is standardized to obtain a standardized probabilistic language decision matrix, whose elements reflect the standardized probabilistic language information.
The entropy weight method is used to calculate the weight value of each attribute. The initial weight of each attribute is corrected according to the formula to obtain the modified attribute weight, and the corrected relative weight is calculated.
The entropy weight method is used to calculate the weight value of each attribute. The initial weight of each attribute is modified according to the formula to obtain the modified attribute weight, and the modified relative weight is calculated.
When the probabilistic linguistic expected value of scheme A on attribute B is greater than the expected value of scheme A', the dominance is positive (determined by the parameters e, λ, etc.). When the expected values of the two scenarios are equal, the dominance may be zero (depending on the specific formula implementation). When the expected value of option A is less than the expected value of option A', the dominance is negative. The calculated dominance under all attributes is aggregated to obtain the comprehensive dominance p(A,A') of scheme A relative to scheme A'. The purpose of standardization is to convert the comprehensive dominance value into a unified scale, which is convenient for subsequent sorting and comparison. A higher value indicates a better overall performance across all attributes, and is therefore considered a better solution.
When the probability linguistic expected value of plan A on attribute B is greater than the expected value of plan A', the dominance is positive (determined by parameters e, λ, etc.). When the expected values of the two plans are equal, the dominance may be zero (depending on the specific formula implementation). When the expected value of plan A is less than the expected value of plan A', the dominance is negative. The calculated dominance under all attributes is aggregated to obtain the comprehensive dominance p(A,A') of plan A relative to plan A'. The purpose of standardization is to convert the comprehensive dominance value into a unified scale to facilitate subsequent sorting and comparison. The larger the value, the better its overall performance on all attributes, and is therefore considered to be a better solution.
2.算例应用(Example application)
In order to select the right industrial control system security supplier, an industrial enterprise in Sichuan Province invited four experts to evaluate five candidate suppliers in four key aspects: safety monitoring and protection, product fit, emergency response time and new product development capabilities. Among them, the emergency response time is a cost-based indicator, meaning that the shorter the response time, the better, while the other three are benefit-based indicators, that is, the better the performance. The experts evaluated each supplier in detail using a linguistic evaluation scale of nine scales, ranging from very poor (EP) to very good (EG). The assessment results are recorded in four tables (Tables 3.56 to 3.59), which summarize each expert's specific evaluation of each supplier in each evaluation dimension, providing an important reference for the company's subsequent decision-making. Finally, follow the above steps to find A3 as the best solution.
In order to select a suitable industrial control system security supplier, an industrial enterprise in Sichuan Province invited four experts to evaluate five candidate suppliers in four key aspects: security monitoring and protection, product fit, emergency response time, and new product development capabilities. Among them, emergency response time is a cost-based indicator, which means that the shorter the response time, the better, while the other three are benefit-based indicators, that is, the better the performance, the better. The experts used a language evaluation scale with nine levels from extremely poor (EP) to very good (EG) to conduct a detailed evaluation of each supplier. The evaluation results are recorded in four tables (Tables 3.56 to 3.59), which summarize each expert's specific evaluation of each supplier in each evaluation dimension, providing an important reference for the company's subsequent decision-making. Finally, according to the above steps, A3 is the best solution.
(4)比较分析(Comparative Analysis)
Specifically, this paper shows the differences between different decision-making methods in ranking solutions through tabular data (Tables 3.75-3.76), but the key point is that the optimal solution that is ultimately determined by all methods is option A. This finding underscores the scientific and validity of the decision-making method, which is able to consistently identify the optimal solution despite the different methods. The paper also points out that except for the PL-VIKOR and PL-PT-TODIM methods, the worst scenarios identified by other decision-making methods are also the same, and they are all scheme A. This information further confirms the commonality of decision-making methods in some aspects. This paper further discusses the possible reasons for the differences between different decision-making methods, including the different reference points based on the decision-making methods, whether to consider the correlation between attributes, whether to consider the psychological behavior of decision-makers, and the advantages and disadvantages of decision-making methods. Together, these factors influence the performance of the decision-making method and the ranking of the final solution. Finally, this paper suggests that decision-makers should choose the appropriate decision-making method according to their actual situation. This reflects the flexibility and importance of the choice of decision-making methods to ensure the scientific and effective nature of the final solution.
Specifically, this article shows the differences in the ranking of solutions by different decision methods through tabular data (Tables 3.75-3.76), but the key point is that the optimal solution finally determined by all methods is Solution A. This finding emphasizes the scientificity and effectiveness of the decision methods, that is, although the methods are different, they can consistently identify the optimal solution. The article also points out that except for the PL-VIKOR and PL-PT-TODIM methods, the worst solutions identified by other decision methods are also the same, which is Solution A. This information further verifies the commonality of decision methods in certain aspects. The article further discusses the possible reasons for the differences between different decision methods, including the different reference points based on the decision methods, whether the correlation between attributes is considered, whether the psychological behavior of the decision maker is considered, and the advantages and disadvantages of the decision methods themselves. These factors jointly affect the performance of the decision methods and the ranking of the final solutions. Finally, the article suggests that in actual decision problems, decision makers should choose appropriate decision methods according to their actual conditions. This reflects the flexibility and importance of the choice of decision methods to ensure the scientificity and effectiveness of the final solution.
三、知识补充（Knowledge Supplementation）
Dominance refers to the degree of relative superiority of a certain program or technology over other programs or technologies under a certain evaluation index. It is a quantitative representation of the advantages and disadvantages between different schemes, which helps decision-makers to understand the performance differences of each scheme more intuitively.
Dominance refers to the relative advantage of a solution or technology over other solutions or technologies under a certain evaluation index. It is a quantitative representation of the relationship between the advantages and disadvantages of different solutions, which helps decision makers understand the performance differences of various solutions more intuitively.
The specific calculation steps are as follows:
The specific calculation steps are as follows:
1. Determine the evaluation indicators: First of all, it is necessary to clarify the specific indicators of the evaluation program or technology, which should be able to objectively reflect the performance characteristics of the program or technology.
1. Determine the evaluation indicators: First, it is necessary to clarify the specific indicators for evaluating the scheme or technology, which should be able to objectively reflect the performance characteristics of the scheme or technology.
2. Data collection and processing: collect the data of each program or technology under each evaluation index, and carry out necessary processing, such as standardization and normalization, to ensure the comparability between the data.
2. Data collection and processing: Collect the data of each scheme or technology under each evaluation indicator, and perform necessary processing, such as standardization and normalization, to ensure the comparability of the data.
3. Calculate the relative advantage: According to the selected evaluation index and data, calculate the relative advantage of each scheme or technology under the index. This typically involves comparing the scores or performance of different programs on the same metric.
3. Calculate relative advantages: Based on the selected evaluation indicators and data, calculate the relative advantages of each solution or technology under the indicator. This usually involves comparing the scores or performance of different solutions under the same indicator.
4. Comprehensive evaluation: Under multiple evaluation indicators, the relative advantages of each program or technology are comprehensively evaluated to obtain the overall superiority. This can be achieved through methods such as weighted summation, analytic hierarchy process, etc.
4. Comprehensive evaluation: Under multiple evaluation indicators, the relative advantages of each solution or technology are comprehensively evaluated to obtain the overall superiority. This can be achieved through weighted summation, hierarchical analysis method, etc.
When choosing the optimal option among multiple alternatives, the dominance can be used as an important decision-making basis. By calculating the superiority of each option, decision-makers can more intuitively understand the pros and cons of each option, so as to make more informed decisions.
When choosing the best option among multiple alternatives, dominance can serve as an important basis for decision-making. By calculating the dominance of each option, decision makers can more intuitively understand the relationship between the advantages and disadvantages of each option and make more informed decisions.
When calculating dominance, it is important to ensure that the data collected is accurate and reliable, and that it is properly processed to ensure comparability between the data.
When calculating dominance, it is necessary to ensure that the collected data is accurate and reliable, and is properly processed to ensure comparability between data.
When comprehensively evaluating the superiority of each scheme or technology, it is necessary to select an appropriate evaluation method and consider the weight relationship between each evaluation index to ensure the rationality and accuracy of the evaluation results.
When comprehensively evaluating the superiority of various solutions or technologies, it is necessary to select an appropriate evaluation method and consider the weight relationship between various evaluation indicators to ensure the rationality and accuracy of the evaluation results.
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Translation: AI translation
References: Baidu, Wenxin Yiyan
Reference: Wei Village. Multi-attribute group decision-making method based on probabilistic language termset theory and its application[D]. Southwestern University of Finance and Economics, 2023.
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