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Zhe Xue (25): 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 Applications (1)".
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Today, the editor brings you
" Zhexue (25): 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 (1)"
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In this issue, we will introduce the multi-attribute group decision-making model and application based on probabilistic language information in the doctoral dissertation "Multi-attribute Group Decision-making Method and Its Application Research Based on Probabilistic Language Terminology Set 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 its application 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 Dice 相似度的概率语言多属性群决策模型(Probabilistic linguistic multi-attribute group decision-making model based on Dice similarity)
1.三种定义(Three definitions)
In Definition 3.1, a language term set called L is defined, which contains multiple elements such as -0, -2, -1, 0, 1, etc. These elements represent different evaluation or decision outcomes and can be combined with probability to form a probabilistic linguistic terminology.
Definition 3.1 in this paper defines a language term set named L, which contains multiple elements such as -0, -2, -1, 0, 1, etc. These elements represent different evaluation or decision results and can be combined with probability to form a probabilistic language term set.
In order to calculate the similarity between two probabilistic language terminology sets, the Probabilistic Language Dice Similarity Measure (PLDSM) is proposed. This measure is based on the traditional definition of Dice similarity, but with appropriate modifications to accommodate the characteristics of the probabilistic language termset. This paper lists several important properties that PLDSM satisfies, including a range of values between 0 and 1, symmetry, and a value of 1 when two probabilistic language terminology sets are exactly the same.
In order to calculate the similarity between two probabilistic language term sets, this paper proposes the probabilistic language Dice similarity measure (PLDSM). This measure is based on the traditional definition of Dice similarity, but is appropriately modified to adapt to the characteristics of probabilistic language term sets. This paper lists several important properties that PLDSM satisfies, including the value range between 0 and 1, symmetry, and the value of 1 when two probabilistic language term sets are exactly the same.
The formula for calculating PLDSM (Equation 3.1) is referenced in Example 3.1, which takes into account the probability of each term in the probabilistic language terminology set and calculates the similarity between the two terminology sets through specific mathematical operations. According to the PLDSM formula, it is necessary to calculate the sum of the products of the probabilities of all corresponding terms in the two term sets and divide by the function value of the length of the two term sets. The calculated PLDSM values reflect the degree of similarity between the two probabilistic language term sets, with values closer to 1 indicating higher similarity and closer to 0 indicating lower similarity.
Example 3.1 quotes the calculation formula of PLDSM (Formula 3.1), which takes into account the probability of each term in the probabilistic language term set and calculates the similarity between the two term sets through specific mathematical operations. According to the PLDSM formula, it is necessary to calculate the sum of the products of the probabilities of all corresponding terms in the two term sets respectively, and then divide it by the function value of the length of the two term sets. The calculated PLDSM value reflects the similarity between the two probabilistic language term sets. The closer the value is to 1, the higher the similarity is, and the closer it is to 0, the lower the similarity is.
In Definition 3.2, PLDSM is a measure used to quantify the similarity between two probabilistic language terminology sets. This measure is an indicator used to quantify the similarity between PL1(P) and PL2(P). The formula is complex, but the basic idea is to calculate the similarity between the terms in the two sets by comparing the probability distributions of the terms at the corresponding positions in the two sets.
In Definition 3.2, PLDSM is a measure used to quantify the similarity between two probabilistic language term sets. This measure is an indicator used to quantify the similarity between PL1(P) and PL2(P). Its calculation formula is relatively complicated, but the basic idea is to calculate the similarity between them by comparing the probability distribution of terms at corresponding positions in the two sets.
The calculation of Definition 3.3 involves the probability distribution of the terms at the corresponding positions in the two probabilistic language terminology sets and a resolution coefficient λ with values ranging from 0≤λ≤1). The formula is summed and normalized to obtain a similarity value between 0 and 1, with higher values indicating greater similarity between two probabilistic language term sets.
The calculation of Definition 3.3 involves the probability distribution of terms at corresponding positions in two probabilistic language term sets, and a resolution coefficient λ (whose value range is 0≤λ≤1). The formula is summed and normalized to finally obtain a similarity value between 0 and 1. The larger the value, the higher the similarity between the two probabilistic language term sets.
Different attributes (or elements) tend to have different importances in practical decision-making problems. For example, in multi-attribute decision-making (MADM), the importance distribution of attributes may be uneven. In this paper, two probabilistic language-based weighted generalized Dice similarity measures (PLWGDSM) are proposed to quantify the similarity between two probabilistic language terminology sets and consider the influence of attribute weights. These two measures comprehensively evaluate the similarity of two probabilistic language terminology sets by calculating the distance (or similarity) between each attribute value and a reference point, combined with their respective weights.
In practical decision-making problems, different attributes (or elements) often have different importance. For example, in multiple attribute decision making (MADM), the importance distribution of each attribute may be uneven. This paper proposes two weighted generalized Dice similarity measures (PLWGDSM) based on probabilistic language to quantify the similarity between two probabilistic language term sets and consider the influence of attribute weights. These two measurement methods comprehensively evaluate the similarity between two probabilistic language term sets by calculating the distance (or similarity) between each attribute value and a reference point and combining their respective weights.
2.具体步骤(Specific steps)
Depending on the nature of the decision problem, the linguistic information matrix is converted into a cost-based (i.e., the lower the cost, the better) or benefit-oriented (i.e., the higher the benefit, the better) decision matrix. This step is to unify the metrics between the different attributes. Standardize cost- and benefit-based decision matrices to ensure that all attributes are compared on the same scale. The purpose of standardization is to eliminate the influence of different dimensions and magnitudes on the outcome of decision-making.
According to the nature of the decision problem, the language information matrix is converted into a cost-type (i.e., the lower the cost, the better) or benefit-type (i.e., the higher the benefit, the better) decision matrix. This step is to unify the measurement standards between different attributes. The cost-type and benefit-type decision matrices are standardized to ensure that all attributes are compared on the same scale. The purpose of standardization is to eliminate the influence of different dimensions and magnitudes on the decision results.
The importance weight of each attribute is calculated using the entropy weight method. The entropy weight method is an objective weighting method, which determines the weight according to the degree of variation of each attribute, and the greater the degree of variation, the greater the impact on the decision-making outcome. Based on the calculated attribute weights and the characteristics of the probabilistic language terminology set, the probabilistic linguistic weighted generalized Dice similarity measure is used to calculate the similarity or distance between different schemes. Based on the calculation results of PLWGDSM, an idealized scheme is determined, which performs optimally in all attributes. Each candidate is compared with the positive ideal scheme of the probabilistic language, and the scheme closest to the positive ideal scheme is selected as the final decision result according to the measurement results of similarity or distance.
The importance weight of each attribute is calculated using the entropy weight method. The entropy weight method is an objective weighting method that determines the weight according to the degree of variation of each attribute. The greater the degree of variation, the greater the impact of the attribute on the decision result. Using the calculated attribute weights and combining the characteristics of the probabilistic language term set, the probabilistic language weighted generalized Dice similarity measure is applied to calculate the similarity or distance between different solutions. Based on the calculation results of PLWGDSM, an idealized solution is determined, which performs best in all attributes. Each candidate solution is compared with the probabilistic language positive ideal solution, and the solution closest to the positive ideal solution is selected as the final decision result based on the measurement results of similarity or distance.
3.算例应用和敏感性分析(Example Application and Sensitivity Analysis)
Through the green supplier selection process of soybean oil procurement by an agri-food company in Chengdu, the operation of GSCM in practical application was demonstrated. After the company passed the initial screening, there are still five candidate suppliers that need to be further evaluated. To this end, the company invited four experts to evaluate and analyze the candidate suppliers from four aspects: service level, product price, product quality and environmental management. Among them, the product price is regarded as a cost-based indicator, i.e., the lower the better, while the other three indicators are benefit-based indicators, i.e., the higher the better. Finally, follow the above steps to select A3 as the best solution.
The operation of GSCM in practical application is demonstrated through the green supplier selection process of a Chengdu agricultural food company purchasing soybean oil. After the company passed the initial screening, there were still 5 candidate suppliers that needed further evaluation. To this end, the company invited 4 experts to evaluate and analyze the candidate suppliers from four aspects: service level, product price, product quality and environmental management. Among them, product price is regarded as a cost-type indicator, that is, the lower the better, while the other three indicators are benefit-type indicators, that is, the higher the better. Finally, according to the above steps, A3 is selected as the best solution.
Finally, the sensitivity analysis of the resolution coefficient in the multi-attribute group decision-making of rate language information is analyzed, and it is pointed out that with the change of the resolution coefficient, the scheme ranking results are significantly different, and it reflects the risk preference of the decision-maker. Decision-makers can choose the appropriate resolution coefficient value according to their own attitude towards risk to ensure the scientificity and rationality of decision-making.
Finally, there is a sensitivity analysis of the resolution coefficient in multi-attribute group decision-making based on linguistic information. It is pointed out that as the resolution coefficient changes, the solution ranking results are significantly different and reflect the risk preference of the decision-maker. Decision makers can choose appropriate resolution coefficient values based on their own attitudes toward risks to ensure the scientificity and rationality of their decisions.
（2）基于 TOPSIS 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 TOPSIS method)
1.具体步骤(Specific steps)
Firstly, the linguistic information matrix is transformed into a probabilistic linguistic decision matrix. Then, in order to eliminate the influence of different attribute dimensions and magnitudes, it is necessary to standardize the probabilistic language decision matrix to obtain a standardized probabilistic language decision matrix.
First, the language information matrix is converted into a probabilistic language decision matrix. Then, in order to eliminate the influence of different attribute dimensions and magnitudes, the probabilistic language decision matrix needs to be standardized to obtain a standardized probabilistic language decision matrix.
Use the entropy weight method (or other appropriate weighting method) to calculate the weights of individual attributes, which reflect the importance of attributes in the decision-making process.
Use the entropy weight method (or other appropriate weight calculation methods) to calculate the weights of each attribute, which reflects the importance of the attribute in the decision-making process.
Based on the standardized probabilistic language decision matrix and attribute weights, the positive and negative ideal schemes of probabilistic language are determined. A positive ideal scenario is one in which all attributes are optimal (or most in line with the decision-maker's expectations), while a negative ideal scenario is one in which all attributes are the worst (or least in line with the decision-maker's expectations).
Based on the standardized probabilistic language decision matrix and attribute weights, the probabilistic language positive ideal solution and negative ideal solution are determined. The positive ideal solution is the solution where all attributes are optimal (or most in line with the decision maker's expectations), while the negative ideal solution is the solution where all attributes are the worst (or least in line with the decision maker's expectations).
The distance between each scheme and the positive and negative ideal schemes is calculated using the Hemming distance (or other appropriate distance metrics), and weighted by considering the attribute weights. Then, based on the weighted positive ideal distance and the weighted negative ideal distance, the relative proximity (PLRCD) of each scheme to the positive ideal scheme is calculated, and the value reflects the proximity of the scheme to the optimal solution. Finally, the schemes were ranked according to the value of Probabilistic Language Relative Closeness (PLRCD), and the scheme with the largest PLRCD value was selected as the optimal scheme.
The distance between each solution and the positive ideal solution and the negative ideal solution is calculated using the Hamming distance (or other appropriate distance measurement method), and the attribute weight is considered for weighted processing. Then, based on the weighted positive ideal distance and the weighted negative ideal distance, the relative closeness (PLRCD) of each solution to the positive ideal solution is calculated. This value reflects the closeness of the solution to the optimal solution. Finally, the solutions are sorted according to the value of the probabilistic linguistic relative closeness (PLRCD), and the solution with the largest PLRCD value is selected as the optimal solution.
2．算例应用(Application examples)
The fire and rescue bureau of a city in Sichuan Province recently conducted a detailed investigation of some local high-rise residential communities, collected data through field visits and interviews, and invited experts to evaluate the status of fire protection facilities, residents' self-rescue capabilities, distance from fire stations, and safe passages, so as to promote the continuous improvement of fire safety work. According to the above steps, A3 is finally the optimal solution
The Fire Rescue Bureau of a city in Sichuan Province recently conducted a detailed investigation of some local high-rise residential areas, collected data through field visits and interviews, and invited experts to evaluate the status of firefighting facilities, residents' self-rescue capabilities, distance from fire stations, and safe passages in order to promote continuous improvement of fire safety work. According to the above steps, A3 is finally concluded as the best solution.
（3）基于 GRA 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 GRA method)
1.具体步骤(Specific steps)
Firstly, the attribute value of the cost type is transformed into the corresponding attribute value of the benefit type. Then, the linguistic information matrix is transformed into a probabilistic linguistic decision matrix.
First, the cost-type attribute values are converted into their corresponding benefit-type attribute values. Then, the language information matrix is converted into a probabilistic language decision matrix.
The processed data is standardized to obtain a standardized probabilistic language decision matrix for subsequent comparison and analysis. The weights of each attribute are calculated using the CRITIC method, which takes into account the correlation between attributes.
The processed data is standardized to obtain a standardized probabilistic language decision matrix for subsequent comparison and analysis. The weight of each attribute is calculated using the CRITIC method, which takes into account the correlation between attributes.
Based on the standardized probabilistic language decision matrix and attribute weights, two decision matrices are constructed: one is used to calculate the "positive gray correlation coefficient sum", and the other is used to calculate the "negative gray correlation coefficient". These two matrices reflect the proximity of each scheme to both positive and negative ideal scenarios. The sum of the overall positive grey correlation coefficients for each scheme with the positive ideal scheme and the overall negative grey correlation coefficient with the negative ideal scheme are calculated.
Based on the standardized probabilistic language decision matrix and attribute weights, two decision matrices are constructed: one is used to calculate the "positive grey correlation coefficient sum", and the other is used to calculate the "negative grey correlation coefficient". These two matrices reflect the degree of proximity of each scheme to the positive ideal scheme and the negative ideal scheme. The overall positive grey correlation coefficient sum of each scheme with the positive ideal scheme, and the overall negative grey correlation coefficient with the negative ideal scheme are calculated.
Using these values, the Probabilistic Language Relative Correlation (PLRCD) for each scenario is further calculated, which is a composite metric that measures how close the scheme is to the optimal solution. According to the value of Probabilistic Language Relative Correlation (PLRCD), all schemes are ranked, and the scheme with the largest PLRCD value is selected as the optimal scheme.
Using these values, we further calculate the probability linguistic relative correlation degree (PLRCD) of each solution, which is a comprehensive indicator used to measure the closeness of the solution to the optimal solution. According to the value of the probability linguistic relative correlation degree (PLRCD), all solutions are sorted and the solution with the largest PLRCD value is selected as the optimal solution.
2. 算例应用和敏感性分析(Example Application and Sensitivity Analysis)
This paper briefly describes the plan to build an electric vehicle charging station in a city in Sichuan Province, and evaluates five candidate locations by experts from four dimensions, such as exhaust emissions and project cost, using a multi-attribute group decision-making model based on probabilistic language information, to select the best construction site. Following the above steps, A2 is the best solution.
The article briefly describes the plan to build an electric vehicle charging station in a city in Sichuan Province, and uses a multi-attribute group decision-making model based on probabilistic language information to evaluate five candidate locations from four dimensions, such as exhaust emissions and project cost, to select the best construction site. According to the above steps, A2 is finally concluded as the best solution.
In this paper, the value of the resolution coefficient is changed to observe the change of the ranking value of each scheme, so as to carry out sensitivity analysis. The resolution coefficient is an important parameter in grey correlation analysis, which is used to adjust the sensitivity of the difference between different indicators. By changing the resolution coefficient, it is possible to test whether the decision result is stable, that is, whether it is susceptible to parameter changes. Finally, the stability and stationarity of the PL-GRA method in dealing with MAGDM problems are verified. This means that the sensitivity analysis proves that the PL-GRA method can produce stable and reliable decision results when dealing with such multi-attribute group decision-making problems, even in the face of different parameter settings or condition changes.
In this paper, by changing the value of the resolution coefficient and observing the changes in the ranking values of each scheme, a sensitivity analysis is performed. The resolution coefficient is an important parameter in grey relational analysis, which is used to adjust the sensitivity of the differences between different indicators. By changing the resolution coefficient, it is possible to test whether the decision result is stable, that is, whether it is easily affected by parameter changes. At the end of the paper, it is mentioned that the stability and stability of the PL-GRA method in dealing with MAGDM problems have been verified. This means that through sensitivity analysis, it is proved that the PL-GRA method can produce stable and reliable decision results when dealing with such multi-attribute group decision-making problems, even in the face of different parameter settings or condition changes.
三、知识补充（Knowledge Supplementation）
Sensitivity analysis refers to an uncertain analysis technique that studies the impact of certain changes in relevant factors on a certain number of key indicators from the perspective of quantitative analysis. Its essence is to explain the law that key indicators are affected by the changes of these factors by changing the values of relevant variables one by one.
Sensitivity analysis is an uncertainty analysis technique that studies the impact of a certain change in related factors on a certain or a group of key indicators from a quantitative analysis perspective. Its essence is to explain the law of the impact of these factors on key indicators by changing the values of related variables one by one.
（1）分析步骤(Analysis steps)
1. Sensitivity analysis indicators: The object of sensitivity analysis is the specific technical scheme and the economic benefits it reflects. Therefore, some economic benefit evaluation indicators of technical solutions (such as EBIT, payback period, return on investment, net present value, internal rate of return, etc.) can be used as sensitivity analysis indicators.
1. Sensitivity analysis indicators: The object of sensitivity analysis is the specific technical solution and the economic benefits it reflects. Therefore, some economic benefit evaluation indicators of the technical solution (such as profit before interest and taxes, payback period, investment return rate, net present value, internal rate of return, etc.) can be used as sensitivity analysis indicators.
2. The target value of the technical solution: Generally, the value of the economic benefit evaluation index under normal conditions is taken as the target value.
Determine the possible range of uncertainties: This is the basis for sensitivity analysis, which needs to be determined based on historical data, market forecasts, etc.
2. Target value of the technical solution: Generally, the value of the economic benefit evaluation indicator under normal conditions is used as the target value.
Determine the possible range of changes in uncertainty factors: This is the basis for sensitivity analysis and needs to be determined based on historical data, market forecasts and other information.
3. The corresponding change value of the evaluation index when the uncertainty factor changes: The impact of the uncertainty factor on the evaluation index is calculated by simulating the change of the uncertainty factor under different scenarios.
3. The corresponding change value of the evaluation indicator when the uncertainty factor changes: By simulating the changes of uncertainty factors in different scenarios, calculate their impact on the evaluation indicators.
4. Sensitivity factors and their degree of influence: According to the calculation results, find out the sensitivity factors that have the greatest impact on the economic benefits of the project, and analyze their influence and sensitivity.
4. Sensitivity factors and their impact: According to the calculation results, find out the sensitivity factors that have the greatest impact on the economic benefits of the project, and analyze their impact and sensitivity.
5. Project risk tolerance: Based on the results of sensitivity analysis, evaluate the project's risk tolerance in the face of uncertain changes.
5. Project risk tolerance: Based on the results of sensitivity analysis, evaluate the risk tolerance of the project when facing changes in uncertainty factors.
(2) Types
Univariate sensitivity analysis is a sensitivity analysis performed when only one factor changes while the other factors remain the same. This method is simple and easy to implement, but it ignores the interaction between the various factors. Multivariate sensitivity analysis is the impact of changes of multiple factors on the evaluation index. This method is closer to the actual situation, but the computational complexity is higher.
Single factor sensitivity analysis is a sensitivity analysis performed when only one factor is changed while other factors remain unchanged. This method is simple and easy to implement, but it ignores the mutual influence between factors. Multi-factor sensitivity analysis is the impact of changes in multiple factors on the evaluation index. This method is closer to the actual situation, but the calculation complexity is higher.
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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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