精讀博士論文基於概率語言資訊的多內容群決策模型及套用（1）

2024-07-26教育

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「喆學（25）：精讀博士論文

【基於概率語言術語集理論的多內容群決策方法及其套用研究】

基於概率語言資訊的多內容群決策

模型及套用（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)"

Welcome to your visit.

本期推文小編將從思維導圖、精讀內容、知識補充三個方面為大家介紹博士論文【基於概率語言術語集理論的多內容群決策方法及其套用研究】的基於概率語言資訊的多內容群決策模型及套用。

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、思維導圖（Mind Map）

二、精讀內容（Intensive reading content）

（1）基於 Dice 相似度的概率語言多內容群決策模型(Probabilistic linguistic multi-attribute group decision-making model based on Dice similarity)

1.三種定義(Three definitions)

文中定義3.1中定義了一個名為L的語言術語集，它包含了-0、-2、-1、0、1等多個元素。這些元素代表了不同的評估或決策結果，並且可以與概率相結合，形成概率語言術語集。

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.

為了計算兩個概率語言術語集之間的相似度，文中提出了概率語言Dice相似測度（PLDSM）。該測度基於Dice相似度的傳統定義，但進行了適當的修改以適應概率語言術語集的特性。文中列舉了PLDSM滿足的幾個重要性質，包括取值範圍在0到1之間、對稱性以及當兩個概率語言術語集完全相同時取值為1等。

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.

範例3.1中參照了PLDSM的計算公式（公式3.1），該公式考慮了概率語言術語集中每個術語的概率，並透過特定的數學運算來計算兩個術語集之間的相似度。根據PLDSM公式，需要分別計算兩個術語集中所有對應術語概率的乘積之和，再除以兩個術語集長度的函數值。計算出的PLDSM值反映了兩個概率語言術語集之間的相似程度，值越接近1表示相似度越高，越接近0表示相似度越低。

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.

定義3.2中PLDSM是一種用於量化兩個概率語言術語集之間相似度的測度。這個測度是用來量化PL1(P)和PL2(P)之間相似度的一個指標。其計算公式較為復雜，但基本思路是透過比較兩個集合中對應位置上的術語的概率分布，來計算出它們之間的相似度。

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.

定義3.3的計算涉及到兩個概率語言術語集中對應位置上的術語的概率分布，以及一個分辨系數λ（其取值範圍為0≤λ≤1）。公式透過求和並歸一化處理，最終得到一個介於0和1之間的相似度值，該值越大表示兩個概率語言術語集之間的相似度越高。

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.

在實際決策問題中，不同的內容（或元素）往往具有不同的重要性。例如，在多內容決策（MADM）中，各內容的重要性分布可能是不均勻的。文章提出了兩種基於概率語言的加權廣義Dice相似測度（PLWGDSM），用於量化兩個概率語言術語集之間的相似度，並考慮內容權重的影響。這兩個測度方法透過計算每個內容值與一個參考點之間的距離（或相似度），並結合各自的權重，來綜合評估兩個概率語言術語集的相似程度。

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.具體步驟(Specific steps)

根據決策問題的性質，將語言資訊矩陣轉換為成本型（即成本越低越好）或效益型（即效益越高越好）的決策矩陣。這一步是為了統一不同內容之間的衡量標準。對成本型和效益型決策矩陣進行標準化處理，確保所有內容在同一尺度上進行比較。標準化的目的是消除不同因次和量級對決策結果的影響。

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.

使用熵權法計算每個內容的重要性權重。熵權法是一種客觀賦權方法，它根據各內容的變異程度來確定權重，變異程度越大的內容對決策結果的影響越大。利用計算得到的內容權重，結合概率語言術語集的特點，套用概率語言加權廣義Dice相似度測度來計算不同方案之間的相似度或距離。基於PLWGDSM的計算結果，確定一個理想化的方案，該方案在所有內容上均表現最優。將每個待選方案與概率語言正理想方案進行比較，根據相似度或距離的度量結果，選擇出最接近正理想方案的方案作為最終決策結果。

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.算例套用和敏感性分析(Example Application and Sensitivity Analysis)

透過成都市某農業食品公司采購大豆油的綠色供應商選擇過程，展示了GSCM在實際套用中的操作。該公司透過初步篩選後，仍有5家候選供應商需要進一步評估。為此，公司邀請了4位元專家從服務水平、產品價格、產品質素和環境管理四個方面對候選供應商進行評價分析。其中，產品價格被視為成本型指標，即越低越好，而其他三個指標為效益型指標，即越高越好。最後按照上述步驟，選出A3為最佳方案。

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.

最後是率語言資訊的多內容群決策中分辨系數的靈敏度分析，指出隨著分辨系數的變化，方案排序結果顯著不同，並反映了決策者的風險偏好。決策者可根據自身對風險的態度選擇適當的分辨系數值以確保決策的科學性和合理性。

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）基於 TOPSIS 方法的概率語言多內容群決策模型(Probabilistic linguistic multi-attribute group decision-making model based on TOPSIS method)

1.具體步驟(Specific steps)

首先，將語言資訊矩陣轉換為概率語言決策矩陣。接著，為了消除不同內容因次和量級的影響，需要對概率語言決策矩陣進行標準化處理，得到標準化的概率語言決策矩陣。

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.

使用熵權法（或其他合適的權重計算方法）來計算各個內容的權重，這些權重反映了內容在決策過程中的重要程度。

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.

基於標準化的概率語言決策矩陣和內容權重，確定概率語言正理想方案和負理想方案。正理想方案是所有內容都達到最優（或最符合決策者期望）的方案，而負理想方案則是所有內容都最差（或最不符合決策者期望）的方案。

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).

利用海明距離（或其他合適的距離度量方法）計算每個方案與正理想方案和負理想方案之間的距離，並考慮內容權重進行加權處理。接著，基於加權正理想距離和加權負理想距離，計算每個方案與正理想方案的相對接近度（PLRCD），該值反映了方案與最優解的接近程度。最後，根據概率語言相對接近度（PLRCD）的值對方案進行排序，選擇PLRCD值最大的方案作為最優方案。

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．算例套用(Application examples)

四川省某市消防救援局近期對當地部份高層住宅小區進行了詳細調查，透過實地考察、訪談等方式收集數據，並邀請專家從消防設施狀態、住戶自救能力、與消防站距離、安全通道情況四個方面進行評估，以推動消防安全工作的持續改進。根據上述的步驟最後得出A3為最優方案

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）基於 GRA 方法的概率語言多內容群決策模型(Probabilistic linguistic multi-attribute group decision-making model based on GRA method)

1.具體步驟(Specific steps)

首先，成本型的內容值轉化為其相應的效益型的內容值。接著，將語言資訊矩陣轉換為概率語言決策矩陣。

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.

對處理後的數據進行標準化，得到標準化的概率語言決策矩陣，以便進行後續的比較和分析。使用CRITIC方法計算各內容的權重，這種方法考慮了內容間的相關性。

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.

基於標準化的概率語言決策矩陣和內容權重，構建兩個決策矩陣：一個用於計算「正向灰色關聯系數和」，另一個用於計算「負向灰色關聯系數」。這兩個矩陣反映了各方案與正理想方案和負理想方案的接近程度。計算每個方案與正理想方案的整體正向灰色關聯系數和，以及與負理想方案的整體負向灰色關聯系數。

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.

利用這些數值，進一步計算每個方案的概率語言相對關聯度（PLRCD），這是一個綜合指標，用於衡量方案與最優解的接近程度。根據概率語言相對關聯度（PLRCD）的值，對所有方案進行排序，選擇PLRCD值最大的方案作為最優方案。

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. 算例套用和敏感性分析(Example Application and Sensitivity Analysis)

文章簡述了四川省某市計劃建設電動汽車充電站，並透過專家從廢氣排放、工程造價等四維度，采用基於概率語言資訊的多內容群決策模型，評估五個候選位置，以選出最佳建設地點。按照上述步驟，最後得出A2為最佳方案。

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.

文中透過改變分辨系數的值，觀察各個方案排序值的變化情況，從而進行敏感性分析。分辨系數在灰色關聯分析中是一個重要的參數，它用於調節不同指標間差異的敏感性。透過改變分辨系數，可以檢驗決策結果是否穩定，即是否容易受到參數變化的影響。文中最後提到驗證了PL-GRA方法處理MAGDM問題的穩定性和平穩性。這意味著透過敏感性分析，證明了PL-GRA方法在處理此類多內容群決策問題時，能夠得出穩定且可靠的決策結果，即使面對不同的參數設定或條件變化。

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、知識補充（Knowledge Supplementation）

敏感性分析是指從定量分析的角度，研究有關因素發生某種變化對某一個或一組關鍵指標影響程度的一種不確定分析技術。其實質是透過逐一改變相關變量數值的方法來解釋關鍵指標受這些因素變動影響大小的規律。

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）分析步驟(Analysis steps)

1.敏感性分析指標：敏感性分析的物件是具體的技術方案及其反映的經濟效益。因此，技術方案的某些經濟效益評價指標（如息稅前利潤、投資回收期、投資收益率、凈現值、內部收益率等）都可以作為敏感性分析指標。

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.技術方案的目標值：一般將在正常狀態下的經濟效益評價指標數值作為目標值。

確定不確定性因素可能的變動範圍：這是進行敏感性分析的基礎，需要基於歷史數據、市場預測等資訊來確定。

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.不確定性因素變動時評價指標的相應變動值：透過模擬不同情境下不確定性因素的變動，計算其對評價指標的影響。

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.敏感性因素及其影響程度：根據計算結果，找出對專案經濟效益影響最大的敏感性因素，並分析其影響程度和敏感性程度。

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.專案承受風險能力：基於敏感性分析的結果，評估專案在面臨不確定性因素變動時的承受風險能力。

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）類別(Types)

單因素敏感性分析為次只變動一個因素而其他因素保持不變時所做的敏感性分析。這種方法簡單易行，但忽略了各因素之間的相互影響。多因素敏感性分析為多個因素的變動對評價指標的影響。這種方法更接近實際情況，但計算復雜度較高。

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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轉譯：AI轉譯

參考資料：百度、文心一言