摘要：In this issue, the editor will introduce the methodology (1) of the journal article "Decarbonised closed-loop supply chains resili
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“慧学（29）：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（1）”
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Today, the editor brings the
"Hui Xue (29): 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 (1)”
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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（1）。
In this issue, the editor will introduce the methodology (1) 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、方法选择（Method selection）
本研究运用DEMATEL方法与ISM-MICMAC方法分别开展分析，并在此基础上进行结果对照，以形成更为全面的结论。ISM-MICMAC属于一种整体性分析工具，其通过二值化（0与1）来判定因素间的关系，进而绘制出影响力图并完成因素分层；而DEMATEL更偏向局部性研究，能够处理区间数据并揭示出直接与间接关系。两种方法在理论框架上存在一定相似性，因此所得结果能够相互支撑，从而提升研究结论的可靠性。
This study employed both the DEMATEL and ISM-MICMAC methods for analysis, comparing their results to form more comprehensive conclusions. ISM-MICMAC is a holistic analysis tool that uses binary values (0 vs. 1) to determine relationships between factors, thereby generating influence maps and stratifying factors. DEMATEL, on the other hand, is more localized, capable of processing interval data and revealing both direct and indirect relationships. The two methods share certain similarities in their theoretical frameworks, allowing their results to mutually support each other and enhance the reliability of the research conclusions.
2、不确定性处理（Uncertainty handling）
在众多处理不确定性的工具中，如HFS、IFS、PyFS、FFS、PFS与SFS等，本研究最终选择以模糊集理论应对不确定性，以防止模型过度复杂化。各类方法的适用情境并不相同，例如，在不存在中立隶属度的情况下，PFS并不合适；而当隶属度与非隶属度之和为1时，模糊集或HFS更具优势；若专家只能提供单一隶属度值，HFS也无法发挥作用。基于这些适用条件的权衡，采用模糊集能够在保证合理性的同时有效处理不确定性与模糊性。
Among numerous tools for managing uncertainty, such as HFS, IFS, PyFS, FFS, PFS, and SFS, this study ultimately chose fuzzy set theory to address uncertainty and prevent overly complex models. Each method has different applicability scenarios. For example, PFS is not suitable when there is no neutral membership; fuzzy sets or HFS are more effective when the sum of membership and non-membership is 1; and HFS is ineffective if experts can only provide a single membership value. Based on these trade-offs, fuzzy sets can effectively handle uncertainty and ambiguity while ensuring rationality.
3、研究框架（Research framework）
本研究的整体框架分为三个阶段。首先，通过文献综述归纳出在COVID-19背景下影响供应链韧性的标准，内容涵盖经济、生态、社会、技术以及产业等多个层面。其次，借助模糊Delphi方法对制药行业闭环供应链（CLSC）的韧性标准进行筛选与确认。最后，运用F-DEMATEL与F-ISM-MICMAC方法，分别探讨指标间的网络关系，并构建分层结构框架。
The overall framework of this study consists of three phases. First, a literature review identifies criteria that influence supply chain resilience in the context of COVID-19, covering multiple dimensions, including economic, ecological, social, technological, and industrial. Second, a fuzzy Delphi method is used to screen and confirm resilience criteria for closed-loop supply chains (CLSCs) in the pharmaceutical industry. Finally, the F-DEMATEL and F-ISM-MICMAC methods are used to explore the network relationships between indicators and construct a hierarchical framework.
4、数据收集（Data collection）
文章的研究的数据来源于最新文献以及伊朗制药供应链中小企业专家的意见。第一阶段基于二手资料建立初步指标清单，随后在第二和第三阶段通过专家反馈获取数据。研究采用滚雪球抽样，共邀请了10位专家参与。入选条件包括：年龄不低于30岁，具有至少3年管理经验和4年以上制药供应链决策经历，同时需具备相关课程或培训背景，并拥有硕士及以上学历。每场讨论均有一名学术专家协助组织。数据收集形式结合结构化问卷与在线访谈：第二阶段问卷填写时间约1小时；第三阶段则在为期两天的线上会议中完成，总计时长约6小时。
The research data for this article was derived from recent literature and the opinions of experts from small and medium-sized enterprises (SMEs) in the Iranian pharmaceutical supply chain. A preliminary list of indicators was established based on secondary data in the first phase, followed by data collection through expert feedback in the second and third phases. A snowball sampling approach was used, with a total of 10 experts invited to participate. Eligibility criteria included: age 30 or above, at least three years of management experience and at least four years of experience in pharmaceutical supply chain decision-making, relevant coursework or training, and a master's degree or higher. Each discussion was facilitated by an academic expert. Data collection was conducted through a combination of structured questionnaires and online interviews: the second phase questionnaire took approximately one hour to complete, while the third phase was completed over two days of online meetings, totaling approximately six hours.
5、模糊集预备知识（Fuzzy set preliminary knowledge）
模糊集最早由Zadeh于1965年提出，用于刻画元素的隶属程度，其核心概念是隶属函数。常见的函数形式包括三角形、梯形和高斯函数，具体选择需综合考虑数值区间、问题规模、数据分布特征、运算复杂度以及专家经验等因素。本研究采用三角形函数，其优势在于对称性良好、峰值清晰、计算简便且存储需求较低，同时这一选择也得到了专家意见与相关文献的支持。三角模糊数（TFN）通常以三元组（l，m，u）表示，当三者相等时即退化为普通数。本文进一步推导了TFN的加、减、乘、除及数倍运算公式，为后续研究提供数学支撑。
Fuzzy sets were first proposed by Zadeh in 1965 to characterize the degree of membership of elements. The core concept is the membership function. Common function forms include triangular, trapezoidal, and Gaussian functions. The specific choice requires a comprehensive consideration of factors such as the numerical range, problem scale, data distribution characteristics, computational complexity, and expert experience. This study uses triangular functions, which have the advantages of good symmetry, clear peaks, simple calculations, and low storage requirements. This choice is also supported by expert opinion and relevant literature. Triangular fuzzy numbers (TFNs) are usually represented by triples (l, m, u), which degenerate into ordinary numbers when the three are equal. This paper further derives the addition, subtraction, multiplication, division, and multiplication formulas of TFNs, providing mathematical support for subsequent research.
三、知识补充（Knowledge supplementation）
1、模糊集理论简介（Introduction to fuzzy set theory）
模糊集理论（又称模糊集合论，简称模糊集）由美国学者 Zadeh 于 1965 年提出，是一种在数学框架下描述和处理模糊现象的方法。该理论将研究对象及其所体现的模糊概念视为特定的模糊集合，并通过构建合适的隶属函数，对这些集合进行运算与变换，从而实现对模糊对象的分析。模糊集合论以模糊数学为基础，主要探讨非精确或不确定现象。客观世界中广泛存在着大量“亦此亦彼”的模糊状态，而该理论正是研究和解释此类现象的重要工具。
Fuzzy set theory (also known as fuzzy set theory or simply fuzzy sets), proposed by American scholar Zadeh in 1965, is a mathematical method for describing and processing fuzzy phenomena. This theory considers the object of study and the fuzzy concepts it embodies as specific fuzzy sets. By constructing appropriate membership functions and performing operations and transformations on these sets, it enables analysis of fuzzy objects. Fuzzy set theory, based on fuzzy mathematics, primarily explores imprecise or uncertain phenomena. Fuzzy states, which are both "this and that," are prevalent in the objective world, and this theory is a crucial tool for studying and explaining such phenomena.
2、模糊集简介（Introduction to fuzzy sets）
模糊集（亦称模糊集合或模糊子集）是用来刻画模糊概念的一类集合。与传统集合不同，普通集合由具备某种明确属性的对象构成，其界限清晰，隶属关系非此即彼；而在现实思维中，大量概念往往模糊不定，如“年轻”“很大”“暖和”“傍晚”等，这些属性无法用简单的“是”或“否”来界定。模糊集合正是指由具有某种模糊属性的对象组成的整体。由于相关概念本身缺乏清晰界限，对象的隶属关系也不再是绝对的。模糊集的提出，使数学方法能够有效应用于模糊现象的处理，并奠定了模糊集合论（在中国通常称为模糊数学）的理论基础。
Fuzzy sets (also known as fuzzy sets or fuzzy subsets) are a type of set used to characterize fuzzy concepts. Unlike traditional sets, which consist of objects with well-defined attributes, their boundaries are clear, and their affiliations are either-or. In real-world thinking, however, many concepts are often vague, such as "young," "large," "warm," and "evening," which cannot be defined with simple "yes" or "no." A fuzzy set is precisely a set composed of objects with fuzzy attributes. Because the relevant concepts themselves lack clear boundaries, the affiliations of the objects are no longer absolute. The introduction of fuzzy sets enabled the effective application of mathematical methods to the treatment of fuzzy phenomena and laid the theoretical foundation for fuzzy set theory (commonly referred to as fuzzy mathematics in China).
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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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