摘要：In this issue, the editor will introduce the methodology (2) of the journal article "Decarbonised closed-loop supply chains resili
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“慧学（32）：精读期刊论文’Decarbonised closed-loop supply chains resilience: examining the impact of COVID-19 toward risk mitigation by a fuzzy multi-layer decision-making framework’方法（2）”
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"Hui Xue (32): Intensive reading of the journal article
‘Decarbonised closed-loop supply chains resilience: examining the impact of COVID-19 toward risk mitigation by a fuzzy multi-layer decision-making framework’ methodology (2)”
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本期推文小编将从思维导图、精读内容、知识补充三个方面为大家介绍期刊论文《Decarbonised closed-loop supply chains resilience: examining the impact of COVID-19 toward risk mitigation by a fuzzy multi-layer decision-making framework》的方法（2）。
In this issue, the editor will introduce the methodology (2) of the journal article "Decarbonised closed-loop supply chains resilience: examining the impact of COVID-19 toward risk mitigation by a fuzzy multi-layer decision-making framework" from three aspects: mind mapping, intensive reading content, and knowledge supplement.
一、思维导图（Mind mapping）
二、精读内容（Intensive reading content）
1、Fuzzy-Delphi方法（Fuzzy-Delphi method）
Fuzzy-Delphi方法是一种群体性知识获取与筛选工具，其核心是通过专家问卷与反馈过程凝聚意见，从而确保研究结果的科学与可靠。在本研究中，研究团队首先归纳出17项受COVID-19影响的制药逆向供应链韧性指标，并邀请10位专家依据五级语言变量对其重要性进行评分。随后，将专家的判断转化为三角模糊数，并采用平均计算得到各指标的模糊权重。接着，通过重心法进行去模糊处理，得到清晰权重，并利用标准差来检验专家意见的一致性（当结果小于0.2时视为共识已形成）。最后，将清晰权重与0.6的阈值进行比对，筛选出需保留的关键指标，以作为后续因果关系分析的输入条件。
The Fuzzy-Delphi method is a group knowledge acquisition and screening tool. Its core is to gather opinions through expert questionnaires and feedback processes to ensure the scientific and reliable research results. In this study, the research team first summarized 17 pharmaceutical reverse supply chain resilience indicators affected by COVID-19 and invited 10 experts to rate their importance based on five-level linguistic variables. Subsequently, the experts' judgments were converted into triangular fuzzy numbers, and the fuzzy weights of each indicator were calculated by averaging. Next, the center of gravity method was used to defuzzify the values to obtain clear weights, and the standard deviation was used to test the consistency of expert opinions (a result less than 0.2 is considered to have reached a consensus). Finally, the clear weights were compared with a threshold of 0.6 to screen out key indicators to be retained as input conditions for subsequent causal relationship analysis.
2、F-DEMATEL方法（F-DEMATEL method）
F-DEMATEL方法主要用于揭示并量化复杂系统中各标准之间的因果联系，从而区分“原因标准”与“结果标准”。在本研究中，专家通过两两比较的方式，利用九级语言变量对各标准的影响程度进行评估，并将结果转化为三角模糊数以构建模糊直接关系矩阵，随后经归一化处理得到模糊初始关系矩阵。与传统方法不同，本研究并未采用单一的去模糊化过程，而是分别计算上下界与中值，形成悲观、中性和乐观三类情境下的模糊总关系矩阵。在此基础上，通过阈值设定得到因果关系网络框架，并进一步测算各标准的重要性指标与净因果效应，从而更为直观地展现标准在CLSC韧性体系中的作用机制与地位。
The F-DEMATEL method is primarily used to reveal and quantify the causal relationships between standards in complex systems, thereby distinguishing between "cause standards" and "effect standards." In this study, experts evaluated the impact of each standard using a pairwise comparison method using nine-level linguistic variables. The results were converted into triangular fuzzy numbers to construct a fuzzy direct relationship matrix, which was then normalized to obtain a fuzzy initial relationship matrix. Unlike traditional methods, this study did not employ a single defuzzification process. Instead, it calculated upper and lower bounds and medians separately to form a fuzzy total relationship matrix for three scenarios: pessimistic, neutral, and optimistic. Based on this, a causal network framework was derived through threshold setting, and the importance index and net causal effect of each standard were further calculated, thereby more intuitively demonstrating the role and status of standards in the CLSC resilience system.
3、F-ISM-MICMAC方法（F-ISM-MICMAC method）
F-ISM-MICMAC方法将解释结构模型（ISM）与MICMAC分析相结合，能够在降低专家意见分歧影响的同时，将模糊关系转化为清晰的层级结构。在研究实施过程中，专家首先依据ISM问卷对标准间的关系进行判断，并采用五级语言变量构建模糊自结构交互矩阵。随后，该矩阵按照规则被转化为模糊可达矩阵，并分别在悲观、中性和乐观三种情境下进行计算，以避免单一去模糊化方式带来的偏差。接着，通过对各标准的驱动力与依赖力进行测算，将其划分为驱动型、依赖型、联结型以及自主型，同时绘制模糊驱动–依赖力图。最后，依据可达集、前置集与公共集的层次分解原则，逐步搭建层级框架，最终形成结构化的制药CLSC韧性标准分级模型，为决策者提供直观且系统的分析工具。
The F-ISM-MICMAC method combines the Interpretive Structural Model (ISM) with MICMAC analysis, mitigating the impact of expert disagreement while transforming fuzzy relationships into a clear hierarchical structure. During the research, experts first judged the relationships between standards based on the ISM questionnaire and constructed a fuzzy self-structuring interaction matrix using five-level linguistic variables. This matrix was then converted into a fuzzy reachability matrix according to rules and calculated under three scenarios: pessimistic, neutral, and optimistic, to avoid biases associated with a single defuzzification approach. Next, the driving and dependent forces of each standard were measured and classified into driving, dependent, connecting, and autonomous types. A fuzzy driving-dependency diagram was also constructed. Finally, based on the hierarchical decomposition principle of reachable sets, precondition sets, and common sets, a hierarchical framework was gradually constructed, ultimately forming a structured pharmaceutical CLSC toughness standard grading model, providing decision makers with an intuitive and systematic analytical tool.
三、知识补充（Knowledge supplementation）
1、三角模糊数的基本概念与应用（Basic concepts and applications of triangular fuzzy numbers）
一般而言，用于衡量评价对象性能的各类指标往往带有一定的模糊性。三角模糊数是一种将含糊不清的语言变量转化为确定数值的方法，将其引入评价过程中，可以有效解决评价对象性能难以精确度量、只能依靠自然语言进行模糊描述的矛盾。
Generally speaking, various indicators used to measure the performance of evaluation objects often have a certain degree of ambiguity. Triangular fuzzy numbers are a method for converting ambiguous linguistic variables into definite numerical values. Introducing them into the evaluation process can effectively resolve the contradiction that the performance of the evaluation object is difficult to measure accurately and can only be described vaguely in natural language.
2、去模糊化方法中的重心法解析（Analysis of the center of gravity method in defuzzification）
重心法是一种常用的去模糊化方法，其基本思想是通过计算模糊集合的重心位置来获得对应的确定值，这一原理与物理学中的质心概念相似。在运算过程中，该方法不仅关注各隶属度的大小，还结合了其对应确定值在数轴上的位置，因此输出结果同时受到隶属度水平和空间分布的影响。具体而言，重心法首先计算每个点的隶属度与其确定值坐标的乘积，并在坐标轴上进行积分，如果是离散情况下可简化为求和，随后以该乘积总和除以隶属度总和，即可得到最终的确定值。由于能够全面反映模糊集合的形状与中心特征，该方法在处理连续分布时尤为有效。总体而言，重心法被普遍认为是一种直观且均衡的去模糊化方式，因为它综合考虑了隶属度整体分布的特性。
The centroid method is a commonly used defuzzification method. Its basic idea is to obtain the corresponding deterministic value by calculating the centroid of a fuzzy set. This principle is similar to the concept of center of mass in physics. During the calculation process, this method not only considers the magnitude of each membership degree but also incorporates the position of its corresponding deterministic value on the number axis. Therefore, the output is influenced by both the level of membership and the spatial distribution of the membership degree. Specifically, the centroid method first calculates the product of each point's membership degree and the coordinates of its deterministic value and integrates them along the coordinate axis. In the discrete case, this can be simplified to a summation. The final deterministic value is then obtained by dividing the sum of these products by the total membership degree. Because it can fully reflect the shape and center characteristics of the fuzzy set, this method is particularly effective when dealing with continuous distributions. Overall, the centroid method is widely considered an intuitive and balanced defuzzification method because it comprehensively considers the characteristics of the overall distribution of membership degrees.
3、模糊矩阵的基本概念与应用（Basic concepts and applications of fuzzy matrix）
在模糊数学中，模糊矩阵是一种用于刻画模糊关系的基本工具，其元素取值限定在零到一之间。当集合X包含若干元素而集合Y也具有一定数量的元素时，二者之间的模糊关系可以表示为一个相应规模的矩阵，并且依据自反性、对称性和传递性等特征进行分类。该矩阵的运算通常采用查德算子，也就是最大最小运算，并被广泛应用于模糊聚类分析和模糊综合评价等研究领域。
In fuzzy mathematics, a fuzzy matrix is a fundamental tool for characterizing fuzzy relationships. Its elements are constrained to range from zero to one. When a set X contains a certain number of elements and a set Y also has a certain number of elements, the fuzzy relationship between the two can be represented as a matrix of corresponding size, classified based on characteristics such as reflexivity, symmetry, and transitivity. Operations on this matrix typically employ the Chad operator, also known as the maximum-minimum operation, and are widely used in research fields such as fuzzy cluster analysis and fuzzy comprehensive evaluation.
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翻译：Google翻译
参考资料：百度、Chatgpt
参考文献： Hannan Amoozad Mahdiraji, Fatemeh Yaftiyan,Jose Arturo Garza-Reyes, et al. Decarbonised closed-loop supply chains resilience: examining the impact of COVID-19 toward risk mitigation by a fuzzy multi-layer decision-making framework [J]. Annals of Operations Research, 2024, 1(1): 1-45.
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