分享兴趣，传播快乐，
增长见闻，留下美好。
亲爱的您，
这里是LearingYard学苑！
今天小编为大家带来
《基于cubic Fermatean模糊集的MARCOS方法及其在评估和选择冷链物流配送中心中的应用》。
欢迎您的访问！
Share interests, spread happiness,
increase knowledge, and leave beautiful.
Dear,
this is the LearningYard Academy!
Today, the editor brings the "MARCOS approach based upon cubic Fermatean fuzzy set and its application in evaluation and selecting cold chain logistics distribution center".
Welcome to visit!
小编将从思维导图、精读内容、知识补充三个板块为大家带来《基于cubic Fermatean模糊集的MARCOS方法及其在评估和选择冷链物流配送中心中的应用》引言。
I will bring you the introduction of MARCOS approach based upon cubic Fermatean fuzzy set and its application in evaluation and selecting cold chain logistics distribution center from three sections: mind mapping, intensive reading content, and knowledge supplementation.
01思维导图
02精读内容
一、背景介绍
I. Background
第一段首先介绍背景。随着决策理论研究的深入和社会经济的快速发展，决策问题变得越来越复杂和多样化。决策群体运用集体智慧进行决策，不仅可以降低决策的风险系数，还可以提高决策的效率和结果的合理性。因此，作为现代决策科学的一个重要分支，多准则群体决策(MCGDM)比传统的多准则决策(MCDM)具有更广泛的适用范围和更高效的决策机制。
The first paragraph begins with the background. With the in-depth study of decision-making theory and the rapid development of society and economy, decision-making problems have become more and more complex and diversified. Decision-making groups use collective wisdom to make decisions, which can not only reduce the risk factor of decision-making, but also improve the efficiency of decision-making and the rationality of the results. Therefore, as an important branch of modern decision-making science, multi-criteria group decision-making (MCGDM) has a wider scope of application and a more efficient decision-making mechanism than the traditional multi-criteria decision-making (MCDM).
二、文献综述
2. Literature review
介绍了模糊集的发展。Zadeh首先提出的模糊集概念，Atanassov在此基础上发展了intuitionistic fuzzy set (IFS)，Yager针对IFS的缺点提出Pythagorean fuzzy set (PFS)，Senapati和Yager通过使隶属度和非隶属度的立方和属于区间[0,1]来扩大信息表达的范围，提出了Fermatean fuzzy set(FFS)。
The development of fuzzy sets is presented.Zadeh first introduced the concept of fuzzy sets, Atanassov developed intuitionistic fuzzy set (IFS) based on it, Yager proposed Pythagorean fuzzy set (PFS) to address the shortcomings of IFS, Senapati and Yager proposed Fermatean fuzzy set (FFS) by making the subordination degree and the cubic sum of the non-affiliated degrees to belong to the interval [0,1] to extend the range of information representation, and proposed Fermatean fuzzy set (FFS).
第二段首先介绍了FFS的优越性，然后介绍了关于FFS的应用可以分为三个方面。
The second paragraph firstly introduces the superiority of FFS and then describes that the applications about FFS can be divided into three areas.
优越性：FFS通过使隶属度和非隶属度的立方和属于区间[0,1]来扩大信息表达的范围。因此，在处理决策问题的不确定性方面，FFS比IFS和PFS更有效、更可行。应用：(1)利用算子对Fermatean模糊信息进行聚类，构造决策方法。(2)将经典决策方法在FFS上进行扩展。(3)将FFS与其他模糊集进行结合拓展FFS理论，或者结合多种决策算法和信息测度来解决实际应用问题。
Superiority: the FFS extends the range of information expression by making the cubic sum of the affiliation and non-affiliation degrees belong to the interval [0,1]. Therefore, FFS is more effective and feasible than IFS and PFS in dealing with uncertainty in decision problems. APPLICATIONS:(1) Clustering Fermatean fuzzy information using operators to construct decision-making methods. (2) Extend the classical decision-making method on FFS. (3) Extend FFS theory by combining FFS with other fuzzy sets, or combine multiple decision-making algorithms and information measures to solve practical application problems.
第三段介绍了cubic模糊集及其应用。cubic模糊集通过两个不同的时区来描述专家的评价观点。由于CFS在不确定信息表达方面的优点，它已被扩展到不同的不确定环境中，并获得了更强大的信息表示模型来解决各种情况下的决策问题。
The third paragraph describes cubic fuzzy set and its applications. cubic fuzzy set describes the expert's evaluative view through two different time zones. Due to the advantages of CFS in the representation of uncertain information, it has been extended to different uncertain environments and gained more powerful information representation models to solve decision-making problems in various situations.
第四段介绍了MACROS方法及其应用。MACROS通过考虑方案与理想和反理想解决方案的相对重要性，进而通过方案的效用函数确定最优方案。该方法的优点是在形成原始决策矩阵时，通过考虑理想解和反理想解，基于稳定的效用度积分函数，确定不同准则下备选方案的优先关系。MARCOS技术的研究已被推广到各种不确定环境中，以构建更强大的决策模型来支持复杂问题的分析。
The fourth paragraph describes the MACROS method and its applications.MACROS determines the optimal solution by considering the relative importance of the solution with respect to the ideal and anti-ideal solutions, and hence the utility function of the solution. The advantage of this method is to determine the priority relationship of alternatives under different criteria by considering both ideal and anti-ideal solutions based on a stable utility integral function when forming the original decision matrix.The research of MARCOS technique has been extended to various uncertain environments to build more powerful decision models to support the analysis of complex problems.
三、研究内容
3. Content of the study
在CFS、FFS和CIFS的激励下，作者开创了一个名为CFFS的创新概念，以阐明评估者的不确定和模糊偏好，该概念由FFS和区间值FFS组成，可以视为对CIFS和CPFS的概括。接下来，基于Aczel-Alsina运算在生成模糊数运算方面的显著优点，通过将Aczel-Alsina运算扩展到CFFS，定义了几种灵活的运算，并提出了一些聚合算子来集成cubic Fermatan模糊信息。在此基础上，针对权重信息完全未知的问题，设计了一种具有两种权重计算方法的综合群体决策方法。
Motivated by CFS, FFS and CIFS, the authors pioneered an innovative concept called CFFS to shed light on the uncertainty and fuzzy preferences of evaluators, which consists of FFS and interval-valued FFS and can be considered as a generalisation of CIFS and CPFS. Next, based on the significant advantages of Aczel-Alsina operations in generating fuzzy number operations, several flexible operations are defined by extending Aczel-Alsina operations to CFFS, and some aggregation operators are proposed to integrate cubic Fermatan fuzzy information. On this basis, an integrated group decision-making method with two weight calculation methods is designed for the problem of completely unknown weight information.
四、文章意图与贡献
4. Intent and contribution of the article
(1)作为cubic set和Fermatan模糊集的有效推广，首次引入了CFFS的概念来表达不确定信息。在此基础上，提出了分数函数、精度函数、比较规则、基本运算和广义cubic Fermatan模糊距离测度。
(2)针对cubic Fermatan模糊数(CFFN)上的Aczel-Alsina运算，提出了一组cubic Fermatan模糊Aczel-Alsina聚合算子，以求一组CFFN的积分值。
(3)基于定义的评分函数和CFFS设置的广义距离，提出了基于评分函数的专家权重算法和基于距离的准则权重识别模型，分别计算专家权重和准则权重。
(4)结合所提出的算子、权值确定算法和扩展的MARCOS方法，提出了一种混合MCGDM框架来选择最佳的CCLDC。
(5)通过一个CCLDC选择问题来阐明所提出的MCGDM框架的可行性和有效性。
(6)通过可行性分析、敏感性分析和对比分析，进一步验证了所提出方法的有效性、可靠性和稳健性。
(1) As an effective generalisation of cubic set and Fermatan fuzzy set, the concept of CFFS is introduced for the first time to express uncertain information. On this basis, fraction function, precision function, comparison rule, basic operation and generalised cubic Fermatan fuzzy distance measure are proposed.
(2) A set of cubic Fermatan fuzzy Aczel-Alsina aggregation operators are proposed for the Aczel-Alsina operation on cubic Fermatan fuzzy numbers (CFFN) to find a set of integral values of CFFN.
(3) Based on the defined scoring function and the generalised distance set by the CFFS, an expert weight algorithm based on the scoring function and a distance-based criterion weight identification model are proposed to compute the expert weights and criterion weights, respectively.
(4) A hybrid MCGDM framework is proposed to select the optimal CCLDC by combining the proposed operator, weight determination algorithm and extended MARCOS method.
(5) The feasibility and effectiveness of the proposed MCGDM framework are elucidated through a CCLDC selection problem.
(6) The validity, reliability and robustness of the proposed method are further verified through feasibility, sensitivity and comparative analyses.
五、文章框架
5. Article framework
第2节简要回顾了几个基本背景知识。第3节提出了CCFS的概念，并进一步给出了CCFS的评分函数、准确率函数、比较规则和广义距离度量。在第4节中，提出一些cubic Fermatan模糊Aczel-Alsina聚集算子，并证明了这些算子的几个重要性质。第5节给出了所提出的cubic Fermatan模糊MARCOS群决策方法的详细过程。第6节以CCLDC的选择为例，利用所提出的方法选择最优的CCLDC，并进行敏感性分析和对比分析，以验证所提出方法的实用性和优越性。最后一节总结了文章的几个结论、局限性和进一步的研究。
Section 2 briefly reviews several basic background knowledge. Section 3 presents the concept of CCFS and further gives the scoring function, accuracy function, comparison rule and generalised distance metric for CCFS. In Section 4, some cubic Fermatan fuzzy Aczel-Alsina aggregation operators are presented and several important properties of these operators are proved. Section 5 gives the detailed procedure of the proposed cubic Fermatan fuzzy MARCOS group decision making method. Section 6 takes an example of CCLDC selection and uses the proposed method to select the optimal CCLDC and performs sensitivity and comparative analyses to verify the practicality and superiority of the proposed method. The last section summarises several conclusions, limitations and further research of the article.
03知识补充
直觉模糊集：
intuitionistic fuzzy set:
毕达哥拉斯模糊集：
Pythagorean fuzzy set:
今天的分享就到这里了。
如果您对今天的文章有独特的想法,
欢迎给我们留言，
让我们相约明天。
祝您今天过得开心快乐！
That's all for today's sharing.
If you have a unique idea bout the article,
please leave us a message,
and let us meet tomorrow.
I wish you a nice day!
参考资料：Deepl、CSDN、百度
参考文献：
[1]Rong Y, Yu L, Niu W, et al. MARCOS approach based upon cubic Fermatean fuzzy set and its application in evaluation and selecting cold chain logistics distribution center [J]. Engineering Applications of Artificial Intelligence, 2022, 116(1): 105401-105427.
[2]陈德江, 王君. 基于直觉模糊集的防空作战目标威胁评估 [J]. 探测与控制学报, 2019, 41(4): 46-51.
[3]曾守桢, 穆志民. 基于混合加权距离的毕达哥拉斯模糊TOPSIS多属性决策方法研究 [J]. 中国管理科学, 2019, 27(3): 198-205.
本文由LearningYard学苑原创，如有侵权请在后台留言！
文字|Zheng
排版|Zheng
审核|wang