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《基于cubic Fermatean模糊集的MARCOS方法及其在評估和選擇冷鍊物流配送中心中的應用》。
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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".
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小編将從思維導圖、精讀内容、知識補充三個闆塊為大家帶來《基于cubic Fermatean模糊集的MARCOS方法及其在評估和選擇冷鍊物流配送中心中的應用》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思維導圖
02精讀内容
一、背景介紹
I. Background
第一段首先介紹背景。随着決策理論研究的深入和社會經濟的快速發展，決策問題變得越來越複雜和多樣化。決策群體運用集體智慧進行決策，不僅可以降低決策的風險系數，還可以提高決策的效率和結果的合理性。是以，作為現代決策科學的一個重要分支，多準則群體決策(MCGDM)比傳統的多準則決策(MCDM)具有更廣泛的适用範圍和更高效的決策機制。
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、文獻綜述
2. Literature review
介紹了模糊集的發展。Zadeh首先提出的模糊集概念，Atanassov在此基礎上發展了intuitionistic fuzzy set (IFS)，Yager針對IFS的缺點提出Pythagorean fuzzy set (PFS)，Senapati和Yager通過使隸屬度和非隸屬度的立方和屬于區間[0,1]來擴大資訊表達的範圍，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).
第二段首先介紹了FFS的優越性，然後介紹了關于FFS的應用可以分為三個方面。
The second paragraph firstly introduces the superiority of FFS and then describes that the applications about FFS can be divided into three areas.
優越性：FFS通過使隸屬度和非隸屬度的立方和屬于區間[0,1]來擴大資訊表達的範圍。是以，在處理決策問題的不确定性方面，FFS比IFS和PFS更有效、更可行。應用：(1)利用算子對Fermatean模糊資訊進行聚類，構造決策方法。(2)将經典決策方法在FFS上進行擴充。(3)将FFS與其他模糊集進行結合拓展FFS理論，或者結合多種決策算法和資訊測度來解決實際應用問題。
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.
第三段介紹了cubic模糊集及其應用。cubic模糊集通過兩個不同的時區來描述專家的評價觀點。由于CFS在不确定資訊表達方面的優點，它已被擴充到不同的不确定環境中，并獲得了更強大的資訊表示模型來解決各種情況下的決策問題。
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.
第四段介紹了MACROS方法及其應用。MACROS通過考慮方案與理想和反理想解決方案的相對重要性，進而通過方案的效用函數确定最優方案。該方法的優點是在形成原始決策矩陣時，通過考慮理想解和反理想解，基于穩定的效用度積分函數，确定不同準則下備選方案的優先關系。MARCOS技術的研究已被推廣到各種不确定環境中，以建構更強大的決策模型來支援複雜問題的分析。
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的激勵下，作者開創了一個名為CFFS的創新概念，以闡明評估者的不确定和模糊偏好，該概念由FFS和區間值FFS組成，可以視為對CIFS和CPFS的概括。接下來，基于Aczel-Alsina運算在生成模糊數運算方面的顯著優點，通過将Aczel-Alsina運算擴充到CFFS，定義了幾種靈活的運算，并提出了一些聚合算子來內建cubic Fermatan模糊資訊。在此基礎上，針對權重資訊完全未知的問題，設計了一種具有兩種權重計算方法的綜合群體決策方法。
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、文章意圖與貢獻
4. Intent and contribution of the article
(1)作為cubic set和Fermatan模糊集的有效推廣，首次引入了CFFS的概念來表達不确定資訊。在此基礎上，提出了分數函數、精度函數、比較規則、基本運算和廣義cubic Fermatan模糊距離測度。
(2)針對cubic Fermatan模糊數(CFFN)上的Aczel-Alsina運算，提出了一組cubic Fermatan模糊Aczel-Alsina聚合算子，以求一組CFFN的積分值。
(3)基于定義的評分函數和CFFS設定的廣義距離，提出了基于評分函數的專家權重算法和基于距離的準則權重識别模型，分别計算專家權重和準則權重。
(4)結合所提出的算子、權值确定算法和擴充的MARCOS方法，提出了一種混合MCGDM架構來選擇最佳的CCLDC。
(5)通過一個CCLDC選擇問題來闡明所提出的MCGDM架構的可行性和有效性。
(6)通過可行性分析、敏感性分析和對比分析，進一步驗證了所提出方法的有效性、可靠性和穩健性。
(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、文章架構
5. Article framework
第2節簡要回顧了幾個基本背景知識。第3節提出了CCFS的概念，并進一步給出了CCFS的評分函數、準确率函數、比較規則和廣義距離度量。在第4節中，提出一些cubic Fermatan模糊Aczel-Alsina聚集算子，并證明了這些算子的幾個重要性質。第5節給出了所提出的cubic Fermatan模糊MARCOS群決策方法的詳細過程。第6節以CCLDC的選擇為例，利用所提出的方法選擇最優的CCLDC，并進行敏感性分析和對比分析，以驗證所提出方法的實用性和優越性。最後一節總結了文章的幾個結論、局限性和進一步的研究。
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知識補充
直覺模糊集：
intuitionistic fuzzy set:
畢達哥拉斯模糊集：
Pythagorean fuzzy set:
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參考資料：Deepl、CSDN、百度
參考文獻：
[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]陳德江, 王君. 基于直覺模糊集的防空作戰目标威脅評估 [J]. 探測與控制學報, 2019, 41(4): 46-51.
[3]曾守桢, 穆志民. 基于混合權重距離的畢達哥拉斯模糊TOPSIS多屬性決策方法研究 [J]. 中國管理科學, 2019, 27(3): 198-205.
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