分享樂趣，傳播快樂，
增加見聞，留下美好！
親愛的您，這裡是LearningYard學苑！
今天小編為大家帶來的文章
“喆學（28）：精讀博士論文
《基于機率語言術語集理論的多屬性群決策方法及其應用研究》
基于機率語言資訊的多屬性群決策
模型及其應用（2）”。
歡迎您的通路。
Share interest, spread happiness,
increase knowledge, and leave beautiful!
Dear, this is LearningYard Academy!
Today, the editor brings you
" 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)"
Welcome to your visit.
本期推文小編将從思維導圖、精讀内容、知識補充三個方面為大家介紹博士論文《基于機率語言術語集理論的多屬性群決策方法及其應用研究》的基于機率語言資訊的多屬性群決策模型及其應用。
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 itsapplication 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、精讀内容（Intensive reading content）
(1)基于 EDAS 方法的機率語言多屬性群決策模型(Probabilistic linguistic multi-attribute group decision-making model based on EDAS method)
1.具體步驟(Specific steps)
首先，将語言資訊轉換為機率語言表示，以便進行量化分析和決策。接着，将語言資訊矩陣中的資料進行标準化處理，以便後續的分析和比較。
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.
利用熵權法來确定多屬性決策問題中各屬性權重的過程。熵權法是一種基于資訊論中熵的概念來客觀計算名額權重的方法，其核心思想是根據各名額變異程度的大小來确定其權重。通過評估各屬性的變異程度來确定其重要性，為決策提供客觀、科學的依據。
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.
對于每個屬性下的所有機率語言值進行平均，以評估該屬性下各方案的平均表現。根據屬性的不同特性（效益型或成本型），使用不同的計算方法得到機率語言正向距離矩陣和負向距離矩陣，以進一步評估各方案之間的相對優劣。
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.
通過計算機率語言正向距離矩陣（PLPDA）和機率語言負向距離矩陣（PLNDA）的權重和，來得到每個方案的機率語言正向得分（PLSP）和機率語言負向得分（PLSN）。接着，對得到的每個方案的 PLSP 和 PLSN 進行标準化處理，以消除量綱差異，得到标準化的 PLSP（PLNSP）和标準化的 PLSN（PLNSN）。最後得到的 PLNSP 和 PLNSN 進行算術平均，得到每個方案的機率語言評估得分（PLAS）并排序。
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. 算例應用(Application examples)
成都市某家電制造企業需要采購一批原材料，并希望從候選供應商中選擇出最優的綠色供應商。經過初步篩選，剩下5家候選供應商需要進一步評估。邀請了4位專家從4個方面對供應商進行評估，包括。供貨能力、服務水準、進貨成本（成本型名額）和企業環境（效益型名額），最後A1為最優方案。
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 方法的機率語言多屬性群決策模型(Probabilistic Linguistic Multi-attribute Group Decision Making Model Based on MABAC Method)
1.具體步驟(Specific steps)
首先，将成本型名額的屬性值轉換為相應的效益型名額的屬性值。然後，建構了一個機率語言決策矩陣Y，它是一個m行n列的矩陣，矩陣中的每個元素PL(g(P))代表了在某個特征值g(P)下對應的第Φ個機率語言資訊，其中Φ的取值範圍是1到#PL(P)，#PL(P)表示在g(P)下可能的機率語言資訊的總數。接下來，對這個機率語言決策矩陣進行了标準化處理，得到了一個新的标準化的機率語言決策矩陣Y'。在标準化過程中，每個元素都被其所在列的平均值所除，以確定所有元素都在同一尺度上進行比較。
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.
首先，需要計算每兩個屬性之間的機率語言相關系數（PLCC），通過這些相關系數，我們可以建構一個機率語言相關系數矩陣（PLCCM），這個矩陣中的元素表示了各屬性對之間的相關性強度。接下來，我們需要計算每個屬性的機率語言标準差（PLSD），标準差是衡量資料分布離散程度的一個名額，在這裡它幫助我們判斷每個屬性在不同情況下的變化程度。在有了相關系數和标準差之後，我們可以根據這些值來計算每個屬性的客觀權重。最後，我們需要将上述計算得到的客觀權重與專家給出的主觀權重結合起來，得到每個屬性的組合權重。
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.
計算每個方案與機率語言邊界逼近區域 PLBAA 之間的機率語言權重海明距離。當PLHD=0時，表示方案A位于機率語言邊界逼近區域PLBAA的邊界上。當PLHD>0時，表示方案A位于上邊界逼近區域PLBAA*，更靠近機率語言正理想方案PLPIS。當PLHD<0時，表示方案A位于下邊界逼近區域PLBAA，更靠近機率語言負理想方案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.
最後，根據機率語言得分值PLSV大小關系對所有的備選方案進行排序比較，最大值所對應的方案為最優方案。
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. 算例應用(Application of calculation examples)
成都市某企業為提升網絡安全性，組織4位專家對5家具備資質的網絡安全服務供應商進行評估，評估涵蓋裝置性能、維護難度（成本型名額）、測評能力及應急支撐能力（均為效益型名額），采用語言資訊标度（極差至非常好）進行評分，以期選出最合适的合作夥伴。最後按照上述步驟得出A4為最優方案。
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)基于前景理論和 TODIM 方法的機率語言多屬性群決策模型(Probabilistic linguistic multi-attribute group decision-making model based on prospect theory and TODIM method)
1.具體步驟(Specific steps)
将成本型名額的屬性值轉化為相應的效益型名額的屬性值，随後将初始的語言資訊矩陣轉換為機率語言決策矩陣，其中的每個元素PL(P)表示在特定條件下的機率語言資訊集合。之後，對機率語言決策矩陣進行标準化處理，得到标準化的機率語言決策矩陣，其元素反映了标準化後的機率語言資訊。
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.
利用熵權法計算每個屬性的權重值。将每個屬性的初始權重按照公式進行修正,進而得到修正的屬性權重,并計算出修正後的相對權重。
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.
當方案A在屬性B上的機率語言期望值大于方案A'的期望值時，占優度為正（由參數e、λ等決定）。當兩個方案的期望值相等時，占優度可能為零（取決于具體的公式實作）。當方案A的期望值小于方案A'的期望值時，占優度為負。計算得到的所有屬性下的占優度進行集結，得到方案A相對于方案A'的綜合占優度p(A,A')。标準化的目的是将綜合占優度值轉換為一個統一的尺度，便于後續的排序和比較。值越大的方案，表示其在所有屬性上的綜合表現越好，是以被認為是更優的方案。
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.算例應用(Example application)
四川省某工業企業為了選擇合适的工業控制系統安全供應商，邀請了4位專家對5家候選供應商在四個關鍵方面進行評估：安全監測保護、産品契合度、應急響應時間以及新産品發展能力。其中，應急響應時間是成本型名額，意味着響應時間越短越好，而其餘三項為效益型名額，即表現越佳越好。專家們使用語言評估标度，從極差（EP）到非常好（EG）共九個等級，對每家供應商進行了詳盡的評估。評估結果分别記錄在四張表格中（表3.56至表3.59），這些表格彙總了每位專家對每家供應商在各評估次元上的具體評價，為企業後續決策提供了重要的參考依據。最後按照上述步驟得出A3為最佳方案。
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)比較分析(Comparative Analysis)
具體來說，這篇文章通過表格資料（表3.75-3.76）展示了不同決策方法在排序解決方案時的差異，但關鍵點是所有方法最終确定的最優方案都是方案A。這一發現強調了決策方法的科學性和有效性，即盡管方法不同，但能夠一緻地識别出最優解。文章還指出了除PL-VIKOR和PL-PT-TODIM方法外，其他決策方法識别的最差方案也相同，均為方案A。這一資訊進一步驗證了決策方法在某些方面的共性。文章進一步讨論了不同決策方法産生差異的可能原因，包括決策方法依據的參照點不同、是否考慮屬性間的關聯性、是否考慮決策者的心理行為以及決策方法自身的優劣特點等。這些因素共同影響了決策方法的表現和最終解決方案的排序。最後，文章建議在實際決策問題中，決策者應根據自身實際情況來選擇合适的決策方法。這反映了決策方法選擇的靈活性和重要性，以確定最終解決方案的科學性和有效性。
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、知識補充（Knowledge Supplementation）
占優度是指某個方案或技術在某一評價名額下，相對于其他方案或技術所表現出的相對優勢程度。它是對不同方案之間優劣關系的一種量化表示，有助于決策者更直覺地了解各方案的性能差異。
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.
具體計算步驟如下：
The specific calculation steps are as follows:
1、确定評價名額：首先，需要明确評價方案或技術的具體名額，這些名額應能夠客觀反映方案或技術的性能特點。
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、資料收集與處理：收集各方案或技術在各評價名額下的資料，并進行必要的處理，如标準化、歸一化等，以確定資料之間的可比性。
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、計算相對優勢：根據所選的評價名額和資料，計算各方案或技術在該名額下的相對優勢。這通常涉及比較不同方案在同一名額下的得分或表現。
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、綜合評估：在多個評價名額下，将各方案或技術的相對優勢進行綜合評估，得出整體的占優度。這可以通過權重求和、層次分析法等方法實作。
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.
在多個備選方案中選擇最優方案時，占優度可以作為重要的決策依據。通過計算各方案的占優度，決策者可以更直覺地了解各方案的優劣關系，進而做出更明智的決策。
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.
在計算占優度時，需要確定所收集的資料準确可靠，并經過适當的處理以確定資料之間的可比性。
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.
在綜合評估各方案或技術的占優度時，需要選擇合适的評估方法，并考慮各評價名額之間的權重關系，以確定評估結果的合理性和準确性。
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.
今天的分享就到這裡了。
如果您對文章有獨特的想法，
歡迎給我們留言，
讓我們相約明天。
祝您今天過得開心快樂！
That's all for today's sharing.
If you have a unique idea about the article,
please leave us a message,
and let us meet tomorrow.
I wish you a nice day!
翻譯：AI翻譯
參考資料：百度、文心一言
參考文獻：衛村. 基于機率語言術語集理論的多屬性群決策方法及其應用研究 [D]. 西南财經大學, 2023.
本文由LearningYard學苑整理發出，如有侵權請在背景留言！
文案|hzy
排版|hzy
稽核|yyz