A Hybrid Hesitant Fuzzy DEMATEL-Entropy Weight Variation Coefficient Method for Low-Carbon Automotive Supply Chain Risk Assessment

Abstract

In the context of a low-carbon economy, automotive parts supply chains face multifaceted risks, making an effective supply chain risk assessment model a crucial means of ensuring supply chain stability. Traditional evaluation methods struggle to comprehensively and accurately identify all influencing factors and their interrelationships in automotive parts supply chains. This article constructs an evaluation model based on the principle of symmetry. The “structural symmetry” is determined by the ratio of the completeness of risk dimension coverage in the indicator system to the precision of indicators, while “fusion symmetry” refers to the degree of equilibrium in information contribution during the fusion of subjective and objective weights. First, Fault Tree Analysis (FTA) and the Delphi method are adopted to establish a risk evaluation index system, whereby structural symmetry is ensured by the equilibrium between the completeness of risk dimension coverage and the accuracy of indicators in the index system. Second, drawing on the symmetric fusion principle, this study proposes a hybrid evaluation approach integrating hesitant fuzzy DEMATEL with entropy weight-coefficient of variation (HDEC), and the fusion symmetry is guaranteed by the balanced integration of subjective and objective weight information. Finally, a case study of an automotive parts supply chain enterprise quantitatively assesses and ranks risk factors, with corresponding countermeasures proposed. The symmetry-guided HDEC method achieves high accuracy, identifying indicator–causal relationships. Compared with the traditional entropy-weighted AHP algorithm, the Pearson correlation coefficient is 0.8566, and Spearman’s rank correlation coefficient is 0.88, indicating strong weight correlation and robust stability. The integration of mathematical symmetry enhances the model’s theoretical rigor, which aligns with symmetry-oriented optimization research.

1. Introduction

As fossil energy sources become increasingly depleted, their large-scale consumption has fueled global economic growth while triggering severe ecological degradation and climate change problems [1]. As a vital pillar of the national economy and a primary source of carbon emissions, the manufacturing sector has emerged as a key area for low-carbon transformation [2]. The low-carbon transition of component manufacturing is particularly critical, as controlling emissions during production, transportation, and storage is essential for optimizing industrial structures and achieving synergistic gains in economic and environmental benefits [3].

In recent years, governments worldwide have successively introduced carbon constraint measures, including mandatory emission policies, carbon tax policies, carbon compensation mechanisms, and carbon trading schemes [4,5,6,7], to regulate carbon emissions in manufacturing and transportation sectors. Consequently, research has focused on carbon emissions during enterprise operations: Zhu W et al. [8] explored optimal operational strategies for enterprises under carbon credit and emission reduction conditions to minimize carbon emissions. Yang Zhou et al. [9] examined multidimensional risks within sustainable coal supply chains, providing scientific decision support for the coal industry to balance supply security and carbon emission reduction. Kharayat S T et al. [10] employed the best-worst method and grey influence analysis to investigate barriers to the widespread adoption of low-carbon technologies in supply chain management, proposing corresponding improvement measures. The theoretical approaches and improvement pathways proposed in these studies provide crucial theoretical foundations and practical guidance for low-carbon supply chain risk management, and has played a positive role in refining and optimizing low-carbon supply chain risk control systems.

Against the dual backdrop of global industrial collaboration and low-carbon transformation, the automotive parts supply chain—as the core support system for the automotive industry—exhibits distinct characteristics: numerous links, extensive scope, and diverse participants. It encompasses not only core segments such as raw material procurement, parts production, warehousing and logistics, and assembly coordination, but also confronts multiple external shocks such as market demand fluctuations, policy and regulatory adjustments, geopolitical shifts, and low-carbon emission constraints. Moreover, the intricate interdependencies and transmission relationships among various links and entities endow supply chain risks with complex attributes including concealment, transmissibility, and superposition. Consequently, the complex supply chain structure necessitates comprehensive identification and analysis across multiple dimensions and stages.

Regarding automotive parts supply chain risk research: Hesam Shidpour et al. [11] adopted multiple machine learning algorithms to predict delay probabilities and determine optimal supplier allocation, thereby reducing supply chain risks. Oliveira D R U et al. [12] carried out the screening and prioritization of SCRM tools for suppliers in the automotive industry through a two-phase approach: first, the Delphi method was adopted to screen and evaluate SCRM tools among 20 s-tier suppliers; then, the Analytic Hierarchy Process was applied to prioritize the candidate tools for first-tier auto parts manufacturers. Yang C et al. [13] focused on coal supply chain risk assessment, established a coal safety indicator system and then developed a risk evaluation model using the Analytic Hierarchy Process (AHP) and Fuzzy Comprehensive Evaluation. Practical application cases demonstrated the AHP-FCE method’s validity and applicability. Runze Y et al. [14] employed a combined quantitative and qualitative approach, extracted EPC project risk factors from literature reviews and expert interviews. They constructed an integrated F-AHP and F-DEMATEL model to analyze the importance and causal relationships of risk factors. Shi J et al. [15] proposed an improved TOPSIS method incorporating loss penalties to evaluate risk levels based on three operational modes of CBEC-SCF and risk analysis. The aforementioned studies focus on risk assessment across diverse supply chain types, encompassing multifaceted research scenarios and rich evaluation methodologies. They have made significant contributions to refining the theoretical framework and advancing practical applications in supply chain risk assessment.

Although existing research has explored numerous avenues for optimizing supply chain risk assessment methods and analyzing their correlation with low-carbon policies, notable shortcomings remain: First, no study has systematically incorporated low-carbon factors as a core dimension in automotive supply chain risk assessment frameworks; second, insufficient attention has been paid to the hesitant characteristics of expert evaluation information; third, it is challenging to effectively balance subjective and objective weights to obtain stable and reliable weights for automotive supply chain risk indicators. Furthermore, current research on automotive parts supply chain risks predominantly focuses on uncertainties and target deviations during supply chain operations. Studies on identifying and assessing supply chain risks under low-carbon constraints remain scarce, failing to meet the practical demands of automotive supply chain risk management in the context of low-carbon transformation.

Addressing the aforementioned research gaps, this paper conducts research on risk identification and evaluation in the automotive parts supply chain under the low-carbon context, based on the symmetry approach. The core of “structural symmetry” lies in the “equilibrium invariance of system coverage and accuracy” [16], with its invariant $S_{struc}=H_{\mathit{cover}}/H_{prec}$ falling within the symmetry interval $\left[0.8,1.2\right]$. The core of “symmetric fusion” lies in the “equilibrium and invariance of subjective and objective information contributions” [17]. Its invariant $S_{fusion}=H_{subj}/H_{obj}$ must satisfy the threshold $S_{fusion}\le 0.1$ to ensure that the weights do not excessively favor one method, leading to an imbalance between subjective and objective weights. Firstly, the risk factors are systematically identified through fault tree analysis, and redundant indicators are screened using the Delphi method to construct a risk evaluation index system that conforms to structural symmetry. Then, guided by symmetry, the HDEC comprehensive evaluation model is proposed. The subjective weight is determined through the hesitant fuzzy DEMATEL method, and the objective weight is determined by combining the entropy weight-coefficient of variation method. The subjective and objective weights are symmetrically integrated, and whether the equilibrium value meets the standard is calculated. Finally, this study validated the proposed method using real-world data from automotive parts enterprises over 2019–2024, demonstrating its effectiveness and feasibility. Compared to traditional approaches, the HDEC model effectively integrates the hesitant-fuzzy characteristics of expert evaluations with historical data variations, enhancing the reliability and stability of assessment outcomes. Furthermore, when contrasted with conventional entropy-weighting-AHP algorithms, it exhibits superior robustness.

2. Construction of the Risk Evaluation Index System for Automotive Component Supply Chains

Risks in the automotive parts supply chain are inherently concealed and contagious. Fault tree analysis (FTA) categorizes events into three core dimensions: top-level events (the problem to be analyzed), intermediate events (the analysis process of influencing factors), and bottom-level events (the root causes of the problem). Treating “supply chain risk events” as top-level events, FTA progressively decomposes them into intermediate and bottom-level events, and uses logical gates (AND, OR) to map causal relationships among risk factors, enabling systematic and thorough identification of potential risks and avoiding indicator omissions of traditional experience-based methods. While FTA identifies root causes comprehensively, some decomposed basic events may possibly have weak correlation or be difficult to measure. Thus, the Delphi method was adopted to conduct multiple rounds of anonymous screening by experts in supply chain management, automotive manufacturing and related fields, eliminating indicators with low correlation or practically difficult data acquisition. Finally, a comprehensive and evaluable automotive supply chain risk evaluation index system with symmetric structure was established.

The specific process is as follows:

(1)

Identify key risk dimensions affecting automotive parts supply chain operations within the context of low-carbon development, establishing the overall direction and research boundaries for risk assessment;

(2)

Using fault tree analysis, define the top-level event of the evaluation system, systematically identify primary failure causes triggering this event, construct the fault tree structure for the automotive parts supply chain, summarize corresponding mid-level events based on prior researchers’ experience, and identify corresponding bottom-level risk events under each mid-level event branch path;

(3)

By combining practical industry expertise with the Delphi method, multiple rounds of assessment and screening were conducted to eliminate redundant indicators that are highly subjective or have low relevance. This ensures the scientific rigor and representativeness of the indicator system, ultimately establishing a comprehensive and actionable risk evaluation framework for automotive parts supply chains.

2.1. Risk Factor Analysis Based on Fault Tree for Automotive Component Supply Chains

Fault Tree Analysis (FTA) is a systematic deductive method for investigating the causes of system failures and identifying potential risks. This method visually presents information in a tree diagram format, decomposing top-level events into contributing factors through logical gates to analyze the causes and occurrence probabilities of system failures [18]. To construct a scientifically effective risk evaluation indicator system for automotive parts supply chains in a low-carbon context, this paper first comprehensively analyzes the potential risks and contributing factors within this supply chain. Subsequently, integrating relevant domestic and international research findings, it expanding the existing research framework by incorporating environmental risks alongside personnel, management, and technological dimensions. Ultimately, five typical supply chain segments [19]—environmental risk (GT1), transportation risk (GT2), logistics risk (GT3), manufacturing risk (GT4), and demand risk (GT5)—were selected for analysis. Key risk factors were identified, and a fault tree model was constructed.

The specific analysis steps are as follows:

(1)

Using fault tree analysis, the top-level event is defined as “unacceptable risks or poor performance occurring in the automotive parts supply chain,” denoted as T.

(2)

Under the top-level event, five categories of intermediate risk events were identified based on actual operational scenarios and risk sources, denoted as $GTi$, which form the first layer of intermediate events in the fault tree.

(3)

Based on the specific characteristics of each intermediate event, further decomposition is conducted to derive mid-level events. Events that cannot be further decomposed are defined as bottom-level events, denoted as $GFi$. Different intermediate events are structurally connected via two types of logic gates, namely AND gates and OR gates, thereby forming a complete fault tree model. The final fault tree model for the auto parts supply chain is illustrated in Figure 1.

Figure 1 presents a fault tree analysis diagram illustrating the causes of risks in the automotive supply chain. This diagram enables the analysis of all root causes of failures based on the top-level event, thereby providing support for the establishment of a risk assessment indicator system. FTA reveals that under the top-level event “Unacceptable risks or poor performance in the automotive parts supply chain”, the minimal cut set includes GT1–GT5. In FTA, an “OR gates” indicates that the failure of any single lower-level event will cause the upper-level event to fail; an “AND gates” indicates that multiple lower-level events must fail simultaneously to cause the upper-level event to fail or be damaged. In this paper’s process of identifying automotive parts supply chain risk factors, “OR gates” are used to connect fault tree nodes when a change in any single supply chain risk factor triggers the upper-level risk event. “AND gates” are used when changes or fluctuations in multiple supply chain risk factors are required to trigger the upper-level risk event. For example: Excessive carbon emissions, low organizational management effectiveness, and low material recycling rates can all trigger environmental risks; thus, an “OR gate” connects environmental risks with their underlying risk events. Low organizational management effectiveness arises from combined factors such as insufficient management system maturity and inadequate technological innovation; therefore, an “AND gate” connects low organizational management effectiveness with its underlying risk events. The relationship construction for factors under other indicators follows the same principle.

Table 1. Risk Events in Automotive Component Supply Chains.

Code	Event	Code	Event
GT1	Environmental Risk	GF6	Excessive transit time
GT2	Transportation Risk	GF7	Inefficient transportation scheduling
GT3	Logistics Risk	GF8	High transportation accident rate
GT4	Manufacturing Risk	GF9	High transportation costs
GT5	Demand Risk	GF10	Freight damage rate
GT6	Carbon Emissions Exceeding Limits	GF11	Low warehouse security
GT7	Organizational Management Inefficiency	GF12	Inadequate safety stock ratio
GT8	Low On-Time Delivery Rate	GF13	Untimely inventory verification
GT9	Low Transportation Efficiency	GF14	High delivery disruption rate
GT10	Warehousing and Inventory Risk	GF15	Insufficient production equipment efficiency
GT11	Cost and Efficiency	GF16	Excessive process production costs
GT12	Insufficient Quality Processes	GF17	Low supplier capacity stability
GT13	Demand Fluctuation Risk	GF18	High defect rate
GT14	Customer Risk	GF19	Inadequate employee expertise
GF1	Production Carbon Emissions Exceeding Limits	GF20	Market demand volatility
GF2	Transportation Carbon Emissions Exceeding Limits	GF21	Policy change impact
GF3	Low Material Recycling Rate	GF22	Threat level of substitutes
GF4	Insufficient Management System Maturity	GF23	Customer order concentration
GF5	Insufficient Technological Innovation	GF24	Customer credit risk

below lists the event codes and corresponding event definitions for the fault tree diagram of the automotive parts supply chain [20]. $G{T}_i$ denote mid-level events, while $G{F}_i$ denote bottom-level events.

Through fault tree analysis, 14 mid-level events and 24 bottom-level events were ultimately identified, with the bottom-level events serving as the initial indicator system for automotive supply chain risk assessment.

Based on the formulas for dimension coverage entropy, and the formula for indicator precision entropy,

$$H_{cover}=-{\sum }_{k=1}^5(n_k/N)\ln (n_k/N)$$

(1)

$$H_{prec}=-{\sum }_{i=1}^N(r_i/R)\ln (r_i/R)$$

(2)

where $n_k$ represents the number of indicators in the kth dimension, N denotes the total number of indicators, $r_i$ signifies the expert correlation score for the ith indicator, and in $R=9$ dictates the maximum score. The calculated structural symmetry degree is $S_{struc}=H_{\mathit{cover}}/H_{prec}=1.72$, which does not meet the structural symmetry requirement. Further optimization is needed using the Delphi method.

2.2. Indicator Screening and Determination Based on the Delphi Method

The Delphi method possesses three key characteristics: anonymity, feedback, and statistical analysis [21]. Anonymity avoids mutual influence among experts, ensuring the independence and objectivity of their opinions. Feedback allows experts to revise their judgments based on group responses across multiple rounds, gradually converging toward consensus. Statistical analysis refines key indicators through data examination, eliminating factors with significant disagreements or low importance, thus improving screening efficiency and the scientific rigor of results. Through fault tree analysis, a preliminary risk assessment indicator system for automotive parts supply chains has been established. Further scientific refinement of this indicator system is required to construct a more representative and actionable risk evaluation framework. To this end, this paper employs the Delphi method to screen and optimize the risk indicators derived from the fault tree. The Delphi method step-by-step flowchart is shown in Figure 2.

Based on the principles of authority, relevance, and representativeness for expert selection, an expert advisory panel was formed, including three professors with over 10 years of experience in logistics and supply chain management and two experts with over five years of experience in corporate management and business consulting. Although the expert panel only includes five members, all are senior scholars and practitioners in supply chain risk assessment, with solid theoretical knowledge and extensive industry experience. They are capable of accurately identifying the core risk characteristics of the automotive parts supply chain, effectively compensating for the limitation of a small number of experts. Panel members were designated as E1, E2, E3, E4, and E5. To ensure the scientific rigor and practical applicability of the final indicator system, the following optimization criteria were established:

(1) If expert scores show significant divergence—measured by Kendall’s W concordance coefficient to assess the consistency of ratings—then when, the indicator should be further discussed or eliminated. The formula for Kendall’s W concordance coefficient is:

$$W={\displaystyle \frac{12{\displaystyle \sum _{i=1}^m{R}_i^2}-3n^{2}m{\left(m+1\right)}^2}{n^{2}m{\left(m^2-1\right)}^2}}$$

(3)

where n is the number of risk indicators, m is the number of experts, and $R_i$ is the sum of the expert ranking scores for the ith indicator;

(2) Indicators demonstrating high consistency and importance across multiple scoring rounds are retained in the final system;

(3) Indicators deemed by most experts to have low relevance to supply chain risk or high data inaccessibility are removed.

First Round of Expert Consultation:

The first round of expert consultation was conducted via questionnaire, distributed from June to July 2024. All expert panel members were required to submit their questionnaires within one week. Experts rated each indicator’s familiarity $F_t$, relevance $R_t$, and importance $I_t$ on a scale of 1–9, with 9 as the highest and 1 the lowest. A weighted sum was calculated for each indicator’s familiarity, relevance, and importance. Weights were assigned based on indicator characteristics: familiarity was weighted at 0.2, while relevance and importance were each weighted at 0.4. The calculation formula for the comprehensive correlation weight $S_t$ is:

$$S_t=0.2\times F_t+0.4\times R_t+0.4\times I_t$$

(4)

Expert E1’s evaluation form is shown in

Table 2. Expert E1 First-Round Questionnaire.

Code Name	Familiarity	Relevance	Importance	Code Name	Familiarity	Relevance	Importance
GF1	6	7	8	GF13	6	6	4
GF2	6	7	8	GF14	9	9	8
GF3	8	9	7	GF15	5	7	7
GF4	7	8	7	GF16	5	6	6
GF5	6	4	6	GF17	6	6	7
GF6	8	7	6	GF18	8	9	8
GF7	8	6	7	GF19	4	7	7
GF8	8	8	8	GF20	5	8	8
GF9	9	9	9	GF21	6	9	9
GF10	8	7	7	GF22	5	4	6
GF11	9	8	6	GF23	8	6	5
GF12	9	7	6	GF24	5	5	5

below, and the detailed scoring data and results of all experts are provided in Appendix A. Based on the scores from the five experts in the first round, the top 15% of indicators by comprehensive relevance weight were retained as highly rated indicators for the final indicator system: Low Material Recycling Rate (GF3), High Transportation Costs (GF9), High Quality Defect Rate (GF18), and Impact of Policy Changes (GF21). Indicators rated as low in accessibility and relevance by experts were removed: Insufficient Technological Innovation (GF5), Untimely Goods Inventory (GF13), Supplier Production Capacity Stability (GF17), and Threat of Substitutes (GF22).

Second Round of Expert Consultation:

Based on the questionnaire model from the first round, the second-round survey questionnaire was designed and distributed in August 2024. All expert panel members were required to submit the questionnaire within one week. This second-round survey aimed to reassess the remaining indicators—excluding those retained for the final set—focusing on their dimensions and redundancy. The questionnaire design addressed three aspects: indicator dimension rationality, redundancy assessment, and integration recommendations. Following the second round of expert consultation, indicators GF1 and GF2 were merged into the new indicator “Carbon Emissions,” indicators GF6 and GF7 were combined into the new indicator “On-Time Rate,” and indicators GF23 and GF24 were consolidated into the new indicator “Customer Risk.” Additionally, due to high information overlap with other indicators, indicators GF12 and GF16 were removed.

Third Round of Expert Consultation:

Based on the outcomes of the first and second rounds, the filtered risk events were distributed via email to all expert panel members in September 2024. Experts conducted reasonableness assessments and indicator conversions, translating risk events into corresponding indicator items and establishing expert consensus.

After three rounds of Delphi questionnaire surveys and data processing, a well-structured and logically coherent risk evaluation index system for automotive parts supply chains was developed. This system balances subjective experience with practical requirements, comprising five levels and 15 risk indicators designated as B1 to B15. The calculated structural symmetry degree is $S_{struc}=1.11$, meeting the symmetry requirements and avoiding the issues of “insufficient coverage” or “excessive redundancy”. The final indicator system is shown in Figure 3.

3. Weight Analysis Model Based on a Hybrid Algorithm

3.1. General Overview of the Proposed Algorithm

In this study, Fault Tree Analysis, the Delphi method, the Hesitant Fuzzy DEMATEL algorithm, and the Entropy Weight-Variation Coefficient method are integrated to establish a comprehensive algorithmic framework covering the entire process from indicator identification and screening to weight calculation. This framework features rigorous logic and high credibility, and thus provides significant reference value for risk assessment of the automotive supply chain.

Firstly, Fault Tree Analysis and the Delphi method are employed to construct a systematic and robust risk assessment indicator system for the automotive supply chain. Subsequently, the Hesitant Fuzzy DEMATEL algorithm is applied to calculate the subjective weights of each risk factor, while the Entropy Weight-Variation Coefficient method is adopted to determine the objective weights. A balance model is then utilized to organically integrate the subjective and objective weights, and the Lagrange function is further used to derive the comprehensive weight of each indicator. The final comprehensive risk assessment model for the supply chain is illustrated in Figure 4. The symmetric fusion of the HDEC model centers around the concept of “balanced contribution of subjective and objective information”. During fusion, $S_{fusion}\le 0.1$ is used as a constraint to prevent symmetry disruption caused by an excessively high proportion of a single weight.

As a subjective weighting algorithm, the Hesitant Fuzzy DEMATEL algorithm can not only fully account for the hesitant fuzziness of expert evaluation information but also effectively identify the causal relationships among risk factors. However, its evaluation results rely heavily on expert experience, which may lead to strong subjectivity and insufficient scientificity and objectivity. To address this limitation, the Entropy Weight-Variation Coefficient method is introduced for objective weighting in this study, which fully explores the volatility and variability of historical data, thereby compensating for the inherent shortcomings of the subjective assessment model.

Figure 4 illustrates the overall process of automotive supply chain risk assessment based on the HDEC algorithm. This process starts with the screening and identification of risk indicators, followed by the construction of a standardized risk assessment indicator system. Subsequently, the comprehensive weight of each indicator is calculated using the evaluation algorithm. Finally, targeted risk improvement strategies are proposed in accordance with the weight distribution results.

3.2. Subjective Weight Determination Based on Hesitant Fuzzy DEMATEL

The hesitant fuzzy DEMATEL algorithm obtains a comprehensive influence matrix by processing expert evaluation information, thereby analyzing the correlation between indicators and calculating the weight of each risk factor indicator. Its key steps include: expert evaluation, hesitant fuzzy processing, direct correlation matrix calculation, comprehensive influence matrix calculation, calculation of row rough numbers and column rough numbers, and calculation of importance and influence degree.

3.2.1. Quantification of Hesitant Fuzzy Sets

Let $L=\left\{l_i\left|i=1,2,\cdots ,n\right.\right\}$ be the set of all possible linguistic terms used to evaluate a given criterion [22], where $l_i$ denotes the ith linguistic level assigned by an expert.

The hesitant linguistic assessment $R_L$ provided by the expert for a specific indicator is an ordered subset of L, denoted as $R_L\in L$.

To quantify the hesitant linguistic terms, let $\lambda \in \left[0,n\right]$ be a numeric set. A mapping function $\mathrm{\Gamma }$ is introduced to establish a one-to-one correspondence between the numerical set and the linguistic set:

$$\mathrm{\Gamma }\left[0,n\right]\to L\times \left[-0.5,0.5\right);\mathrm{\Gamma }\left(\lambda \right)=\left(l_i,{\alpha }_i\right)$$

(5)

where $i=round\left(\lambda \right),l_i=round\left(\lambda \right),{\alpha }_i=\lambda -i,{\alpha }_i\in \left[-0.5,0.5\right)$. Here, $round\left(.\right)$ is the rounding operator, and ${\alpha }_i$ represents the symbolic offset. Then, the semantics can be transformed into corresponding numerical values through the inverse function ${\mathrm{\Gamma }}^{-1}$.

3.2.2. Expert Information Processing Based on Rough Sets

Rough set theory enables efficient computation and comparative analysis of linguistic information. By constructing approximation spaces and applying upper and lower approximation sets, it provides a systematic approach to quantifying and processing imprecise linguistic data. One of its main advantages lies in the fact that it relies solely on the inherent structure of the data under analysis, without requiring any additional subjective input. This characteristic allows rough set theory to effectively model uncertainty while maintaining a high degree of objectivity.

Let U be the universe of discourse consisting of all objects in the evaluation information table, and let $J=\left\{e_1,e_2,\cdots e_m\right\}$ be a set of m classification elements, where $e_1<e_2<\cdots <e_m$.

The lower and upper approximation domains of an element $e_k$ are defined as follows:

$$\underset{¯}{Apr\left(e_k\right)}=U\left\{A\in U\left|J\left(A\right)\le e_k\right.\right\}$$

(6)

$$\overline{Apr\left(e_k\right)}=U\left\{A\in U\left|J\left(A\right)\ge e_k\right.\right\}$$

(7)

The lower and upper boundaries of the element $e_k$ are defined as follows:

$$\overline{\lim \left(e_k\right)}={\displaystyle \frac{{\displaystyle \sum _{i=1}^{C_U}{x}_i}}{C_U}}$$

(8)

$$\underset{¯}{\lim \left(e_k\right)}={\displaystyle \frac{{\displaystyle \sum _{i=1}^{C_L}{y}_i}}{C_L}}$$

(9)

In Equations $x_i$ and $y_i$ represent the elements in the lower and upper approximation domains, respectively. $C_U$ and $C_L$ denote the total number of elements in the upper and lower approximation sets, respectively.

Based on Equations (6)–(9), all elements in set J are transformed into rough numbers as follows:

$$e_k\to \left[\underset{¯}{\lim \left(e_k\right)},\overline{\lim \left(e_k\right)}\right]$$

(10)

The hesitant linguistic terms ${\mathrm{\Gamma }}^{-1}\left(R_L\left(v_i\right)\right)$ are then quantified using rough set theory and converted into rough number sets. The rough boundary interval of the linguistic term can be obtained using Equation (11):

$${\mathrm{\Gamma }}^{-1}\left(R_L\left(v_i\right)\right)=\left[\underset{¯}{M_i},\overline{M_i}\right]=\left[\sqrt[n]{\underset{¯}{\lim \left(l_1\right)}\times \cdots \times \underset{¯}{\lim \left(l_n\right)}},\sqrt[n]{\overline{\lim \left(l_1\right)}\times \cdots \times \overline{\lim \left(l_n\right)}}\right]$$

(11)

Assuming the weight coefficient of the kth expert is ${\omega }_k$, the aggregated rough number of expert evaluations is calculated using Equation (12):

$${\mathrm{\Gamma }}^{-1}\left(R_L\left(v_i\right)\right)=\left[{\displaystyle \sum _{k=1}^n{\omega }_k\times \underset{¯}{M_k},}{\displaystyle \sum _{k=1}^n{\omega }_k\times \overline{M_k}}\right]$$

(12)

3.2.3. Supply Chain Risk Weight Analysis Based on Hesitant Fuzzy DEMATEL

The hesitant fuzzy DEMATEL method [23] is used to analyze the interrelationships among risk factors and determine their relative importance. The specific steps are as follows:

Step 1: Construct the direct-relation matrix $R^k$. Suppose there are m risk factors forming the set G:

$$G=\left\{g_i\left|i=1,2,\cdots ,m\right.\right\}$$

(13)

where $g_i$ denotes the ith risk factor.

Assume there are n experts participating in the evaluation, and the set of their weights is denoted as:

$$H=\left\{{\omega }_j\left|j=1,2,\cdots ,n\right.\right\}$$

(14)

The kth expert applies the semantic sets in

Table 3. Expert Z1 Semantic Judgment Matrix.

	B1	B2	B3	B4	B5	B6	B7	B8	B9	B10	B11	B12	B13	B14	B15
B1	VH	N	L	N	H	N	N	L	N	L	L	N	VL	L	N
B2	VH	H	H	H	N	N	N	N	N	VH	L	N	N	N	N
B3	VH	H	H	N	L	VL	N	L	N	N	N	L	VL	N	N
B4	L	N	N	VH	H	L	L	N	VL	N	N	N	N	N	L
B5	VH	VH	H	N	VH	N	N	N	H	N	N	N	L	H	VL
B6	N	N	N	N	H	VH	L	L	L	N	L	L	N	N	VL
B7	N	N	N	H	N	VH	H	VL	VH	N	VL	N	N	N	VL
B8	L	L	N	N	L	H	N	H	L	N	L	L	L	N	VL
B9	L	VH	N	VH	L	N	L	N	H	N	N	N	L	N	N
B10	VH	H	L	H	L	L	N	N	N	H	VH	VH	H	N	N
B11	L	L	VH	N	H	VL	N	N	N	H	L	VH	H	N	L
B12	N	VL	N	H	N	H	VL	H	H	VH	H	L	N	N	N
B13	N	L	N	N	H	N	L	N	L	VH	VH	H	H	VH	L
B14	VH	H	VH	N	H	H	N	L	N	VH	H	N	VH	VH	VL
B15	N	N	N	H	VL	N	N	L	N	H	H	L	N	N	L

to evaluate the importance of m risk factors and the degree of association among them [24], yielding the direct association matrix of risk factors:

$$R^k=\left[\begin{array}{cccc}{r}_{11}^k& r_{12}^k& \cdots & r_{1m}^k\\ r_{21}^k& r_{22}^k& \cdots & r_{2m}^k\\ ⋮& ⋮& ⋮& ⋮\\ r_{m1}^k& r_{m2}^k& \cdots & r_{mm}^k\end{array}\right]$$

(15)

Here, $r_{ij}^k$ represents the linguistic evaluation given by the kth expert for the degree of influence between risk factors $g_i$ and $g_j$. When $i=j$ the value corresponds to the expert’s assessment of the importance of risk factor $g_i$ itself. The evaluation semantic set is shown in Appendix B.

Based on Equations (4) and (5), each element in the matrix $R^k$ is quantified using ${\mathrm{\Gamma }}^{-1}\left(r_{ij}^k\right)$. Then, applying Equations (6)–(11), the corresponding rough numbers are derived for each element, which are used to construct the rough relationship matrix.

$${\mathrm{\Gamma }}^{-1}\left(R^k\right)=\left[\begin{array}{cccc}\left[\underset{¯}{r_{11}^k},\overline{r_{11}^k}\right]& \left[\underset{¯}{r_{12}^k},\overline{r_{12}^k}\right]& \cdots & \left[\underset{¯}{r_{1m}^k},\overline{r_{1m}^k}\right]\\ \left[\underset{¯}{r_{21}^k},\overline{r_{21}^k}\right]& \left[\underset{¯}{r_{22}^k},\overline{r_{22}^k}\right]& \cdots & \left[\underset{¯}{r_{2m}^k},\overline{r_{2m}^k}\right]\\ ⋮& ⋮& ⋮& ⋮\\ \left[\underset{¯}{r_{m1}^k},\overline{r_{m1}^k}\right]& \left[\underset{¯}{r_{m2}^k},\overline{r_{m2}^k}\right]& \cdots & \left[\underset{¯}{r_{mm}^k},\overline{r_{mm}^k}\right]\end{array}\right]$$

(16)

According to Equation (12), the expert evaluations are aggregated to obtain the group direct-relation matrix of supply chain risk factors, expressed as follows:

$$r_{ij}=\left[{\displaystyle \sum _{k=1}^n{\omega }_k\times \underset{¯}{r_{ij}^k},{\displaystyle \sum _{k=1}^n{\omega }_k\times \overline{r_{ij}^k}}}\right]$$

The resulting direct-relation matrix R is defined as:

$$R=\left[\begin{array}{cccc}{r}_{11}& r_{12}& \cdots & r_{1m}\\ r_{21}& r_{22}& \cdots & r_{2m}\\ ⋮& ⋮& ⋮& ⋮\\ r_{m1}& r_{m2}& \cdots & r_{mm}\end{array}\right]$$

(17)

Step 2: Normalize the direct-relation matrix.

Normalization is performed using the maximum value of the row sums of the matrix RRR as the scaling factor, denoted by $MAX(sum)$. Let the normalized matrix be $N={\left[x_{ij}\right]}_{n\times n}$, where $x_{ij}=\left[\underset{¯}{x_{ij}},\overline{x_{ij}}\right]$, and:

$$Max\left(sum\right)=\max \left({\displaystyle \sum _{i=1}^n{r}_{ij}}\right)$$

(18)

$$\overline{x_{ij}}={\displaystyle \frac{\overline{r_{ij}}}{Max\left(sum\right)}}$$

(19)

Step 3: Compute the total influence matrix

The normalized direct-relation matrix is decomposed into a lower bound matrix $\underset{¯}{N}={\left[\underset{¯}{x_{ij}}\right]}_{n\times n}$ and an upper bound matrix $\overline{N}={\left[\overline{x_{ij}}\right]}_{n\times n}$:

$$\underset{¯}{N}={\left[\underset{¯}{x_{ij}}\right]}_{n\times n},\overline{N}={\left[\overline{x_{ij}}\right]}_{n\times n}$$

(20)

Let the total influence matrix be denoted as T:

$$T={\left[t_{ij}\right]}_{n\times n}$$

(21)

where $t_{ij}$ represents the total influence degree of risk factor $g_i$ on $g_j$. The rough total influence between the two factors is expressed as:

$$t_{ij}=\left[\underset{¯}{t_{ij}},\overline{t_{ij}}\right]$$

(22)

Then, the lower and upper bounds of the total influence matrix T can be calculated using the following equations:

$$\begin{array}{l}\underset{¯}{T}={\left[\underset{¯}{t_{ij}}\right]}_{n\times n}=\underset{¯}{N}{\left(I-\underset{¯}{N}\right)}^{-1},\\ \overline{T}={\left[\overline{t_{ij}}\right]}_{n\times n}=\overline{N}{\left(I-\overline{N}\right)}^{-1}\end{array}$$

(23)

Step 4: Calculate the row-based and column-based rough indices ${\tilde{x}}_i$ and ${\tilde{y}}_j$ from the total influence matrix T.

$$\begin{array}{l}{\tilde{x}}_i={\displaystyle \sum _{j=1}^n{t}_{ij}},i=1,2,\cdots n;\\ {\tilde{y}}_j={\displaystyle \sum _{i=1}^n{t}_{ij}},j=1,2,\cdots n\end{array}$$

(24)

Here, the row rough index ${\tilde{x}}_i$ indicates the influence of risk factor $g_i$ on other risk factors, while the column rough index ${\tilde{y}}_j$ reflects the degree to which $g_j$ is influenced by the other risk factors.

Step 5: Refine the rough index into precise values

To accurately and visually compare the importance of risk factors, rough numbers are normalized and converted into precise numbers ${\tilde{x}}_i^t$ and ${\tilde{y}}_j^t$. The specific steps are detailed in Appendix B.

Step 6: Calculate the importance of each risk indicator

Based on the difference between the influence degree and the influenced degree of risk factor $g_i$, the indicator $R{a}_i$ is introduced to classify risk factors into two categories:

$$R{a}_i={\tilde{x}}_i^t-{\tilde{y}}_i^t$$

(25)

When $R{a}_i>0$, the factor $g_i$ is considered a cause-type risk factor; otherwise, it is categorized as an effect-type risk factor.

Assuming the overall importance of each risk factor is represented by a vector set $Q_i$, we define:

$$Q_i={\tilde{x}}_i^t+{\tilde{y}}_i^t$$

(26)

Here, $Q_i$ reflects the overall importance of risk factor $g_i$. A higher ${\tilde{x}}_i^t$ indicates that the risk factor has a greater impact on other factors, potentially serving as a root cause of chain reactions. Conversely, a higher ${\tilde{y}}_j^t$ implies the risk factor is more susceptible to the influence of other risks and thus more sensitive to system changes. Therefore, a larger $Q_i$ signifies greater importance of the risk factor.

Finally, the normalized importance values $Q_i$ are used to determine the subjective weights ${\eta }_i$ of the risk factors based on the hesitant fuzzy DEMATEL method.

$${\eta }_i={\displaystyle \frac{Q_i}{{\displaystyle \sum _{i=1}^n{Q}_i}}}$$

(27)

3.3. Objective Weight Determination Based on the Entropy and Coefficient of Variation Method

The entropy weight method determines indicator weights based on information entropy, emphasizing the degree of data dispersion. However, it does not account for correlations between indicators. In contrast, the coefficient of variation method measures the relative variability of data to assign weights, focusing solely on internal dispersion while being sensitive to outliers. In the context of automotive supply chain risk evaluation, integrating both methods allows for an objective adjustment and refinement of subjectively obtained weights. This hybrid approach supplements and optimizes the subjectively derived weights, ultimately yielding more accurate risk indicator weights.

3.3.1. Entropy Weight Method

The entropy weight method is grounded in information entropy theory [25], which evaluates indicators by quantifying uncertainty and disorder within the data. The computational procedure includes the following steps:

Step 1: Normalize the original data

All indicators are first categorized as either benefit-type (positive) or cost-type (negative). Then, the data are normalized using Equations (28) and (29), respectively.

$$y_{ij}={\displaystyle \frac{r_{ij}-r_{j\min }}{r_{j\max }-r_{j\min }}}$$

(28)

$$y_{ij}={\displaystyle \frac{r_{j\max }-r_{ij}}{r_{j\max }-r_{j\min }}}$$

(29)

In the formula, $y_{ij}$ represents the dimensionless value of the i indicator for the j year in the automotive parts supply chain. $r_{ij}$ denotes the raw value of the i indicator for the j year in the automotive parts supply chain; $r_{j\max }$ indicates the maximum raw data value for indicator ith; $r_{j\min }$ denotes the minimum raw data value for indicator i.

For each indicator of supplier j, the normalized proportion value $Y_{ij}$, indicating the share of sample j in indicator, is calculated as follows:

$$Y_{ij}={\displaystyle \frac{y_{ij}}{{\displaystyle \sum _{i=1}^m{y}_{ij}}}}$$

(30)

Step 2: Compute the information entropy of each indicator

$${\mathrm{e}}_i=-{\displaystyle \frac{I}{\ln m}}{\displaystyle \sum _{j=1}^m{Y}_{ij}\ln Y_{ij}}$$

(31)

where m represents the number of risk factors in the automotive parts supply chain. To ensure the validity of the calculation: When $Y_{\mathrm{ij}}=0$, then $Y_{\mathrm{ij}}\ln Y_{ij}=0$; $\mathrm{i}=1,2,3\dots m;j=1,2,3\dots n$.

Step 3: Information Utility Values for Each Indicator $d_i$

Information utility reflects the value and role of information in evaluation, decision-making, and other processes. A higher information utility value indicates that the corresponding indicator is more important within the automotive parts supply chain and carries greater significance for evaluation purposes.

$$d_i=1-e_i$$

(32)

Step 4: Compute the weight of each indicator

$$w_{1i}={\displaystyle \frac{d_i}{{\displaystyle \sum _{i=1}^m{d}_i}}}$$

(33)

A larger entropy value for a given indicator suggests that its evaluation values across different alternatives tend to be similar, implying it provides less discriminative information and should be assigned a lower weight. Conversely, a smaller entropy value indicates greater variation in the indicator’s performance across alternatives, contributing more informative content to the evaluation and thus warranting a higher weight. In essence, the entropy weight method highlights the local differences in the same indicator across samples as a reflection of its relative importance.

3.3.2. Coefficient of Variation Method for Weight Calculation

The coefficient of variation method determines the weight of each indicator directly based on statistical characteristics of the data. Specifically, the coefficient of variation is defined as the ratio of the standard deviation to the mean of an indicator, which provides an objective measure of its variability. The detailed calculation procedure is as follows [26]:

Based on Equations (22) and (23), the standardized data are obtained. The standard deviation $S_i$ and the mean ${\overline{k}}_i$ of the ith indicator are calculated as follows:

$$S_i=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{j=1}^n\left(k_{ij}-{\overline{k}}_i\right)}}{n-1}}}$$

(34)

$${\overline{k}}_i={\displaystyle \frac{{\displaystyle \sum _{j=1}^n{k}_{ij}}}{n}}$$

(35)

The coefficient of variation $v_i$ for the ith indicator is then calculated as:

$$v_i={\displaystyle \frac{S_i}{\overline{k_i}}}$$

(36)

Finally, the normalized weight $w_{2i}$ of each evaluation indicator is given by:

$$w_{2i}={\displaystyle \frac{v_i}{{\displaystyle \sum _{i=1}^m{v}_i}}}$$

(37)

3.3.3. Combined Weighting Method Based on Entropy and Coefficient of Variation

According to the principle of minimum information entropy [27], the weights determined by the traditional entropy method and the coefficient of variation method are integrated to obtain a combined weight ${\gamma }_i$. The objective function based on the minimum information entropy model is constructed as follows:

$$\min F={\displaystyle \sum _{i=1}^m{\gamma }_i}\left(\ln {\gamma }_i-\ln w_{1i}\right)+{\displaystyle \sum _{i=1}^m{\gamma }_i}\left(\ln {\gamma }_i-\ln w_{2i}\right)$$

(38)

subject to: ${\displaystyle \sum _{i=1}^m{\gamma }_i=1},{\gamma }_i>0$, Here, F represents the objective function of the minimum entropy optimization model.

By applying the Lagrange multiplier method, the closed-form solution to the above optimization problem can be obtained as:

$${\gamma }_i={\displaystyle \frac{\sqrt{w_{1i}\cdot w_{2i}}}{{\displaystyle \sum _{i=1}^m\sqrt{w_{1i}\cdot w_{2i}}}}}$$

(39)

where ${\gamma }_i$ denotes the final combined weight, $w_{1i}$ is the weight derived from the entropy method, and $w_{2\mathrm{i}}$ is the weight obtained from the coefficient of variation method.

3.4. Comprehensive Weight Calculation Based on HDEC

To ensure the consistency of subjective and objective weight preferences and obtain ideal comprehensive weights, this study adopts the Euclidean distance minimization criterion to construct a weight integration model. Compared with traditional weight combination methods such as multiplicative combination and Manhattan distance, this model has obvious advantages, including: firstly, it can fully reflect the consistency between the two sets of weights and avoid the excessive interference of single-dimensional deviations on the comprehensive weights; secondly, it has moderate sensitivity to weight deviations, good robustness, and is not easily affected by extreme weight values; thirdly, the objective function constructed based on Euclidean distance is continuously differentiable and can be solved analytically by the Lagrange multiplier method, with clear calculation logic and strong interpretability.

Based on the above advantages, this study constructs an objective function combined with Euclidean distance [28], and solves the equations simultaneously through the Lagrange function. The specific steps are as follows:

Step 1: Construct the objective function based on the Euclidean distance between DEMATEL subjective weights ${\eta }_i$ and HDEC combined weights ${\gamma }_i$:

$$\min F={\displaystyle \sum _{i=1}^n{\left({\eta }_i-{\gamma }_i\right)}^2}$$

(40)

Step 2: Define the constraints based on weight normalization and consistency between subjective and objective weighting:

$${\displaystyle \sum _{i=1}^n{w}_i}=1,w_i\ge 0$$

(41)

$$w_i=\alpha {\eta }_i+\beta {\gamma }_i,\alpha +\beta =1$$

(42)

$$S_{fusion}=|H_{subj}-H_{obj}|\le 0.1$$

(43)

Here, $\alpha$ and $\beta$ are preference coefficients that reflect the relative importance of subjective and objective weights, respectively. $H_{subj}$ and $H_{obj}$ represent the subjective and objective weight information entropy, respectively, with the calculation formula as follows.

$$H_{subj}=-{\sum }_{i=1}^{15}{\eta }_i\ln {\eta }_i, H_{obj}=-{\sum }_{i=1}^{15}{\gamma }_i\ln {\gamma }_i$$

(44)

Step 3: Construct the Lagrangian function

To incorporate both the objective function and the constraints, the following Lagrangian function J is formulated:

$$J={\displaystyle \sum _{i=1}^n{\left(w_i-{\eta }_i\right)}^2}+{\displaystyle \sum _{i=1}^n{\left(w_i-{\gamma }_i\right)}^2}+\epsilon \left(1-{\displaystyle \sum _{i=1}^n{w}_i}\right)+\varphi \left(\alpha +\beta -1\right)$$

(45)

where $\epsilon$ and $\phi$ are the Lagrange multipliers, $w_i$ and ${\gamma }_i$ are the subjective and combined weights, respectively, $w_i$ is the final fused weight of the ith indicator.

Step 4: Compute the partial derivatives and solve the system of equations

By taking partial derivatives of with respect to all variables $w_i,\alpha ,\beta ,\epsilon ,\varphi$, and setting each derivative to zero, the system of equations can be solved simultaneously to obtain the optimal values of $w_i$, $\alpha$, and $\beta$.

4. Example

This paper conducts a risk analysis of 15 indicators across five dimensions—low-carbon initiatives, transportation, logistics, manufacturing, and demand—within the automotive parts supply chain. After extracting supply chain data from a specific automotive enterprise spanning 2019 to 2024, it evaluates the risk indicators and proposes corresponding countermeasures. Data sources: National Public Science Data Center for Basic Disciplines: Analysis of automotive supply chain cooperative relationships is based on the “Automotive Supply Chain Cooperative Relationship Dataset (Version v1.0)”. This dataset was constructed by Liu Xin, created by Sichuan University, and released through the National Public Science Data Center for Basic Disciplines on 25 February 2025 (Science and Technology Resource Identifier: CSTR:16666.11.nbsdc.wntlcfeD). The dataset originates from Aipusuo Auto Network and official public materials of parts enterprises, encompassing multi-dimensional information such as automotive parts enterprise attributes, main products, and supporting customers. It provides critical data support for analyzing the relationship network and value chain evolution process among “suppliers-manufacturers- customers” within the supply chain.

4.1. Determining Indicator Weights Using the Hesitant Fuzzy DEMATEL Method

To obtain authentic and reliable assessment results, five experts and scholars with extensive knowledge and experience in the machinery and logistics industries were invited, designated as Z1, Z2, Z3, Z4, and Z5. Each expert conducted relevance evaluations of the 15 selected automotive supply chain risk indicators using verbal terminology. The evaluation results from Expert Z1 are shown in Table 3. The meanings represented by the letters N, VL, L, H, and VH are shown in the semantic set of expert evaluations in Appendix B.

According to Equation (5), the semantic evaluations of supply chain risk indicators by experts are quantified through inverse functions. Equations (6) to (12) process the expert evaluation information based on rough set theory, converting the quantified hesitant fuzzy evaluations into rough sets. This yields a direct association matrix for each expert’s indicator evaluations, which is then weighted and integrated using Equations (16) and (17). Each expert assigned a weight of 0.2. The resulting direct correlation matrix R for the risk factor group evaluation is:

$$R=\left[\begin{array}{cccccc}\left[7.831,8.674\right]& \left[0.000,0.000\right]& \left[0.000,0.000\right]& \cdots & \left[1.569,2.896\right]& \left[0.000,0.000\right]\\ \left[6.340,7.827\right]& \left[6.641,7.960\right]& \left[4.896,5.587\right]& \cdots & \left[0.000,0.000\right]& \left[0.000,0.000\right]\\ \left[8.763,9.632\right]& \left[5.348,6.125\right]& \left[4.682,5.488\right]& \cdots & \left[0.000,0.000\right]& \left[0.000,0.000\right]\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ \left[7.869,8.541\right]& \left[5.548,6.362\right]& \left[6.475,7.548\right]& \cdots & \left[7.257,7.896\right]& \left[1.046,2.348\right]\\ \left[0.000,0.000\right]& \left[0.000,0.000\right]& \left[0.000,0.000\right]& \cdots & \left[0.000,0.000\right]& \left[4.457,5.176\right]\end{array}\right]$$

By normalizing the group evaluation direct correlation matrix R using Formulas (18) to (20), we obtain matrix N and decompose it into lower bound $\underset{¯}{N}$ and upper bound $\overline{N}$ according to the upper and lower limits, as follows:

$$\underset{¯}{N}=\left[\begin{array}{cccccc}0.0574& 0& 0.0271& \cdots & 0.0115& 0\\ 0.0464& 0.0487& 0.0359& \cdots & 0& 0\\ 0.0650& 0.0414& 0.0343& \cdots & 0& 0\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ 0.0577& 0.0407& 0.0488& \cdots & 0.0532& 0.0077\\ 0& 0& 0& \cdots & 0& 0.0327\end{array}\right]·\overline{N}=\left[\begin{array}{cccccc}0.0643& 0& 0.0319& \cdots & 0.0212& 0\\ 0.0574& 0.0584& 0.0410& \cdots & 0& 0\\ 0.0721& 0.0486& 0.0403& \cdots & 0& 0\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ 0.0647& 0.0486& 0.0566& \cdots & 0.0579& 0.0172\\ 0& 0& 0& \cdots & 0& 0.0409\end{array}\right]$$

Performing matrix operations on the lower bound $\underset{¯}{N}$ and upper bound $\overline{N}$ obtained by normalizing the direct association matrix via Equations (21) to (23) yields the comprehensive influence matrix T, as shown below:

$$T=\left[\begin{array}{cccccc}\left[0.0674,0.0801\right]& \left[0.0052,0.0097\right]& \left[0.0335,0.0424\right]& \cdots & \left[0.0142,0.0267\right]& \left[0.0016,0.0039\right]\\ \left[0.0613,0.0791\right]& \left[0.0567,0.0706\right]& \left[0.0449,0.0540\right]& \cdots & \left[0.0012,0.0027\right]& \left[0.0019,0.0036\right]\\ \left[0.0768,0.0898\right]& \left[0.0485,0.0607\right]& \left[0.0409,0.0503\right]& \cdots & \left[0.0024,0.0049\right]& \left[0.0012,0.0031\right]\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ \left[0.0891,0.0986\right]& \left[0.0575,0.0751\right]& \left[0.0653,0.0805\right]& \cdots & \left[0.0625,0.0715\right]& \left[0.0128,0.0273\right]\\ \left[0.0082,0.0128\right]& \left[0.0061,0.0098\right]& \left[0.0056,0.0082\right]& \cdots & \left[0.0013,0.0023\right]& \left[0.0364,0.0475\right]\end{array}\right]$$

Based on the total influence matrix T, the row and column rough indices $\widetilde{x_i}$ and $\widetilde{y_j}$ were calculated using Equation (24). These rough indices were then transformed into precise values ${\tilde{x}}_i^{der}$ and ${\tilde{y}}_j^{der}$ according to Equations (25) and (26). Finally, the importance $Q_i$ and external influence degree $R_{a_i}$ of each risk factor were computed. The detailed calculation results are shown in

Table 4. Calculation of Risk Indicator Importance.

Risk Factor	$\widetilde{{\mathit{x}}_{\mathit{i}}}$	${\tilde{\mathit{x}}}_{\mathit{i}}^{\mathit{d}\mathit{e}\mathit{r}}$	$\widetilde{{\mathit{y}}_{\mathit{j}}}$	${\tilde{\mathit{y}}}_{\mathit{j}}^{\mathit{d}\mathit{e}\mathit{r}}$	${\mathit{R}}_{{\mathit{a}}_{\mathit{i}}}$	${\mathit{Q}}_{\mathit{i}}$	Rank
B1	$\left[0.2443,0.3487\right]$	0.2443	$\left[0.5926,0.7656\right]$	0.6695	−0.4252	0.9138	5
B2	$\left[0.3330,0.4263\right]$	0.3332	$\left[0.4685,0.6238\right]$	0.5157	−0.1825	0.8489	7
B3	$\left[0.3010,0.4167\right]$	0.3023	$\left[0.3754,0.4709\right]$	0.3845	−0.0822	0.6868	10
B4	$\left[0.2596,0.3487\right]$	0.2598	$\left[0.4609,0.5118\right]$	0.4214	−0.1616	0.6812	11
B5	$\left[0.3909,0.5100\right]$	0.3948	$\left[0.4965,0.6555\right]$	0.5496	−0.1549	0.9445	3
B6	$\left[0.3215,0.4160\right]$	0.3229	$\left[0.3982,0.5120\right]$	0.4162	−0.0933	0.7392	9
B7	$\left[0.2656,0.3598\right]$	0.2657	$\left[0.1845,0.2756\right]$	0.1852	0.0805	0.4510	15
B8	$\left[0.3543,0.4665\right]$	0.3558	$\left[0.2718,0.3693\right]$	0.2769	0.0789	0.6328	13
B9	$\left[0.3070,0.4071\right]$	0.3071	$\left[0.3397,0.4421\right]$	0.3496	−0.0425	0.6567	12
B10	$\left[0.5512,0.6979\right]$	0.5745	$\left[0.4669,0.5896\right]$	0.4946	0.0799	1.0693	1
B11	$\left[0.4428,0.5805\right]$	0.4552	$\left[0.4775,0.6248\right]$	0.5209	−0.0657	0.9762	2
B12	$\left[0.3766,0.4890\right]$	0.3785	$\left[0.3789,0.4812\right]$	0.3907	−0.0123	0.7693	8
B13	$\left[0.5035,0.6698\right]$	0.5340	$\left[0.3715,0.4923\right]$	0.3905	0.1435	0.9246	4
B14	$\left[0.6483,0.8337\right]$	0.7069	$\left[0.1973,0.2546\right]$	0.1973	0.5096	0.9043	6
B15	$\left[0.3043,0.3974\right]$	0.3069	$\left[0.1881,0.2988\right]$	0.1909	0.1160	0.4979	14

.

Finally, the subjective weight ${\eta }_i$ for the automotive parts supply chain risk indicators was normalized using formula (27), as shown in

Table 5. Subjective Weights of Indicators Based on the Hesitant Fuzzy DEMATEL Method.

Indicator	B1	B2	B3	B4	B5	B6	B7	B8
Weight	0.0781	0.0762	0.0587	0.0582	0.0808	0.0632	0.0386	0.0541
Indicator	B9	B10	B11	B12	B13	B14	B15
Weight	0.0561	0.0914	0.0835	0.0658	0.0790	0.0773	0.0426

:

Taking $Q_i$ as the horizontal axis and $R_{a_i}$ as the vertical axis, a distribution diagram of the risk factors is drawn, as shown in Figure 5. According to the $R_{a_i}$ calculation formula for the difference between influence and affectedness, the upper half of the vertical axis represents cause-type indicators, while the lower half represents effect-type indicators. The circular markers in the diagram denote the top five key risk indicators.

The indicator causality diagram presented in Figure 5 can clearly distinguish between cause-type indicators and result-type indicators, and complete regional division according to the correlation degree among indicators. As shown in the figure, among the 15 automotive supply chain risk indicators selected through screening: “Transportation Accident Rate,” “Warehouse Security,” “Production Equipment Efficiency,” “Market Demand Fluctuation,” “Policy Changes,” and “Customer Risk” all exhibit positive correlation coefficients $R_{a_i}$, thus qualifying as causal indicators. Among these causal indicators, B14 “Policy Changes” exhibits the highest correlation coefficient of 0.5096. This indicates that B14 exerts a greater influence on the entire automotive supply chain process, as policy shifts directly impact supply chain operations including production, sales, and transportation. Among the effect indicators, B1 “Carbon Emissions” has the lowest correlation coefficient $R_{a_i}$, indicating that B1 is most susceptible to influences from other indicators. Significant fluctuations in B1 suggest major changes in one or all segments of the supply chain. Indicator B10, “Production Equipment Efficiency,” holds the highest importance at 1.0693, indicating its efficiency value changes exert greater influence on the overall system evaluation. Additionally, it is noted that the importance $Q_i$ and external correlation $R_{a_i}$ values for indicators B3, B6, and B9 are similar, indicating comparable levels of influence on the entire process.

Among the risk indicators, the five items “carbon emissions”, “transportation costs”, “production equipment efficiency”, “quality processes”, and “market demand fluctuations” are key risk factor indicators. This may be because low-carbon environmental protection is a core national policy of China, and the continuous implementation of relevant policies has imposed relatively high requirements on enterprises’ low-carbon transformation.

Among them, “carbon emissions” are constrained by emission control policies and environmental standards, and policy changes will directly affect enterprises’ compliance costs and operational stability; “production equipment efficiency” and “quality processes” are core methods for energy conservation and carbon reduction. Inefficient equipment and outdated processes are accompanied by high energy consumption and carbon emissions, which fail to meet current policy requirements and will lead to risks for enterprises in their low-carbon transformation; from an operational perspective, “transportation costs” can reflect the resource consumption intensity of the transportation link, and the degree of their fluctuations indirectly reflects operational risks related to carbon emissions; while “market demand fluctuations” affect the restructuring of market demand. The current upgrading of market preferences for low-carbon products and the adaptation requirements of supply chain systems have further amplified their operational impact on transforming enterprises, constituting a key external market risk.

4.2. Weight Calculation Based on the Entropy and Coefficient of Variation Method

(1) Entropy Weight Calculation

Through data collection and preprocessing, raw data for automotive parts supply chain risk indicators from 2019 to 2024 were obtained. The raw data were categorized into positive indicators and negative indicators based on their nature, as shown in

Table 6. Raw Data for Risk Indicator Factors from 2019 to 2024.

Indicator	2019	2020	2021	2022	2023	2024	Indicator Type
Carbon Emissions (B1)	448	572	688	509	693	586	Negative
Organizational Management Efficiency (B2)	M3	M3	M4	M4	M4	M5	Positive
Material Recycling Rate (B3)	54.64%	59.12%	60.34%	65.78%	64.02%	65.71%	Positive
On-Time Delivery Rate (B4)	83.23%	95.17%	80.23%	93.14%	90.60%	86.54%	Positive
Transportation Cost (B5)	0.0423	0.3542	0.0297	0.0613	0.0443	0.0495	Negative
Cargo Damage Rate (B6)	382.3	408.7	488.1	393.6	410.6	387.5	Negative
Transportation Accident Rate (B7)	0.053%	0.059%	0.062%	0.058%	0.058%	0.062%	Negative
Warehouse Safety (B8)	Qualified	Above Average	High	Very High	Qualified	Above Average	Positive
Delivery Interruption Rate (B9)	0.0083%	0.0071%	0.0077%	0.0075%	0.0073%	0.0074%	Negative
Equipment Efficiency (B10)	0.787	0.783	0.806	0.954	0.898	0.945	Positive
Process Quality (B11)	Q6	Q6	Q5	Q7	Q7	Q6	Positive
Staff Professionalism (B12)	Qualified	Qualified	Qualified	Qualified	Qualified	Highly efficient	Positive
Market Demand Volatility (B13)	0.048	0.019	0.044	0.049	0.036	0.055	Negative
Policy Changes (B14)	3	5	3	5	1	6	Negative
Customer Risk (B15)	Very low	Relatively low	Relatively low	low	low	Very low	Negative

.

The core criterion for classifying positive and negative indicators lies in the direction of correlation between changes in indicator values and the level of supply chain risks. If an increase in the indicator value can reduce supply chain risks and improve the operational stability of the supply chain, it is identified as a positive indicator; otherwise, it is a negative indicator.

For the qualitative indicator data presented in

Table 7. Risk Factor Indicator Values for 2019 to 2024.

Indicator	2019	2020	2021	2022	2023	2024
B1	1.0000	0.4939	0.0204	0.7510	0.0000	0.4367
B2	0.0000	0.1579	0.7895	0.7368	0.6316	1.0000
B3	0.0000	0.4022	0.5117	1.0000	0.8420	0.9937
B4	0.2008	1.0000	0.0000	0.8641	0.6941	0.4224
B5	0.6013	0.8190	1.0000	0.0000	0.5380	0.3734
B6	1.0000	0.7505	0.0000	0.8932	0.7325	0.9509
B7	1.0000	0.3789	0.0000	0.4316	0.4947	0.0316
B8	0.1803	0.2869	0.8197	1.0000	0.0000	0.4426
B9	0.0000	1.0000	0.5000	0.6667	0.8333	0.7500
B10	0.0234	0.0000	0.1345	1.0000	0.6725	0.9474
B11	0.5061	0.2378	0.0000	0.9329	1.0000	0.8171
B12	0.0000	0.3077	0.5385	0.5385	0.6923	1.0000
B13	0.1944	1.0000	0.3056	0.1667	0.5278	0.0000
B14	0.2000	0.2000	0.6000	0.2000	1.0000	0.0000
B15	1.0000	0.0000	0.3333	0.6667	0.6667	1.0000

, to better meet the sensitivity requirements of the entropy weight-coefficient of variation method for minor data fluctuations, the true values of the indicators were further retrieved through semantic analysis. These qualitative data were then converted into quantitatively expressed indicator values and subjected to a normalization process, with detailed indicator data provided in Appendix C. Based on the converted quantitative values of each indicator, data standardization was performed using Equations (28) and (29), and the final results are shown in Table 7.

Standardized processing yields risk factor indicator values in the same dimensionality. Subsequently, formulas (30) and (31) calculate the proportion of the j sample value under the i indicator relative to that indicator, thereby obtaining the entropy values for each indicator. Formulas (32) and (33) compute the utility values for each indicator and normalize them to derive the weights for the 15 risk indicators in the automotive parts supply chain, as shown in

Table 8. Entropy-Based Weights of Each Indicator.

Indicator	B1	B2	B3	B4	B5	B6	B7	B8
Entropy	0.7623	0.8362	0.8657	0.8329	0.8678	0.8940	0.7574	0.8039
Weight	0.0885	0.0610	0.0500	0.0622	0.0492	0.0395	0.0903	0.0730
Indicator	B9	B10	B11	B12	B13	B14	B15
Entropy	0.8842	0.7060	0.8445	0.8602	0.7735	0.7628	0.8632
Weight	0.0431	0.1095	0.0579	0.0521	0.0843	0.0883	0.0509

.

(2) Weight Calculation Based on the Coefficient of Variation Method

Calculate the standard deviation and mean value for each indicator item based on the data in Table 7. Using formulas (34) to (37), compute the coefficient of variation and weight for each indicator. The results are shown in

Table 9. Weight Calculation Based on the Coefficient of Variation Method.

Indicator	Standard Deviation	Mean	Coefficient of Variation	Weight
B1	96.9075	582.6667	0.1663	0.0830
B2	0.0740	0.5350	0.1382	0.0690
B3	0.0439	0.6160	0.0713	0.0356
B4	0.0583	0.8815	0.0661	0.0330
B5	0.0110	0.0438	0.2525	0.1260
B6	39.0505	411.8000	0.0948	0.0473
B7	0.000035	0.0006	0.0590	0.0295
B8	46.9628	876.5000	0.0536	0.0267
B9	0.000004	0.000076	0.055408	0.027659
B10	0.0796	0.8622	0.0923	0.0461
B11	0.6626	6.4450	0.1028	0.0513
B12	4.4121	61.6667	0.0715	0.0357
B13	0.0128	0.0418	0.3067	0.1531
B14	1.8348	4.1667	0.4404	0.2198
B15	0.0117	0.3617	0.0323	0.0161

:

(3) Combined Objective Weight

Based on the principle of minimum information entropy, the weights of risk factor indicators determined by the entropy weight method and coefficient of variation method are coupled using Equations (38) and (39) to obtain the objective composite weight ${\gamma }_i$, as shown in

Table 10. Combined Objective Weights Based on the Entropy–Coefficient of Variation Method.

Indicator	B1	B2	B3	B4	B5	B6	B7	B8
Weight	0.0911	0.0690	0.0448	0.0482	0.0837	0.0460	0.0549	0.0470
Indicator	B9	B10	B11	B12	B13	B14	B15
Weight	0.0367	0.0755	0.0579	0.0458	0.1208	0.1481	0.0305

.

From the table above, the ranking of indicator weights is as follows: B14 > B13 > B1 > B5 > B10 > B2 > B11 > B7 > B4 > B8 > B6 > B12 > B3 > B9 > B15. The five risk factors with the highest weights in the historical data analysis, calculated using the objective combination weighting method, are “carbon emissions,” “policy changes,” “production equipment efficiency,” “market demand fluctuations,” and “transportation accident rate.”

4.3. Comprehensive Weighting

According to Equations (40) to (45), the Euclidean distance method was used to integrate the subjective weights ${\eta }_i$ obtained from the hesitant fuzzy DEMATEL method with the objective weights ${\gamma }_i$ derived from the entropy–coefficient of variation method. A decision model was established to ensure consistency between subjective preferences and objective information. The preference coefficients obtained from the Lagrange function are $\alpha =0.5408,\beta =0.4592$, and by calculating the symmetry fusion degree, we can obtain $S_{fusion}=0.0834$ that satisfies the symmetry fusion constraint. Accordingly, the comprehensive weights of each indicator are shown in

Table 11. Comprehensive Weights of Each Indicator.

Indicator	B1	B2	B3	B4	B5	B6	B7	B8
Weight	0.0852	0.0706	0.0512	0.0528	0.0824	0.0539	0.0474	0.0502
Indicator	B9	B10	B11	B12	B13	B14	B15
Weight	0.0456	0.0828	0.0697	0.0550	0.1016	0.1156	0.0360

.

The comparison of subjective weights, objective weights, and comprehensive weights is illustrated in Figure 6.

Figure 6 takes the risk factor indicators of the automotive supply chain as the horizontal axis, compares the weight values of each risk factor under three different algorithms, and can provide preliminary reference for the subsequent evaluation of algorithm performance based on the fluctuation degree of the curves. The HDEC method proposed in this study achieves accurate risk indicator weighting through a subjective-objective integration logic: subjectively, it performs hesitant fuzzy processing on expert evaluations and uses DEMATEL analysis to derive the correlation relationships and weight trends of each indicator; objectively, it integrates the entropy weight method and coefficient of variation method, fully considering data dispersion and volatility to supplement and revise the weights obtained from subjective evaluation. This addresses the limitation of traditional single methods that fail to simultaneously cover both “correlation logic” and “data facts”. For instance, for B8 “Warehouse Safety”, the DEMATEL method assigns a high base weight based on the “severity of safety risks”, while the entropy weight method appropriately lowers the weight due to the “low data volatility” of this indicator. The final weight not only reflects the “importance of safety” but also aligns with the “current operational safety level”, making it more consistent with actual risks. Indicator B14 “Policy Changes” exhibits the largest subjective-objective weight difference, and the discrepancy stems from the inherent logical characteristics of the two methods: in subjective evaluation, experts consider policy changes as macro external factors that exert an indirect impact on the supply chain through intermediate links such as production and logistics, resulting in a lower weight due to weak direct correlation; objectively, the intensive introduction of low-carbon policies in recent years has led to significant fluctuations in the historical data of this indicators.

Based on the above analytical approach, the five most critical indicators for enterprises in identifying automotive parts supply chain risks under a low-carbon context are: “policy changes,” “market demand fluctuations,” “carbon emissions,” “production equipment efficiency,” and “transportation accident rates.”

4.4. Risk Mitigation Strategies for the Automotive Supply Chain

Conduct a countermeasure analysis of the top five factors most significantly impacting automotive parts supply chain risks in a low-carbon context. The following recommendations are proposed [29]:

(1)

Optimize production technologies and adopt low-carbon practices. Enterprises should continuously improve production equipment and processes to align with national goals of environmental protection and low carbon. Additionally, technologies such as IoT and big data can be used to monitor logistics in real time and enable intelligent scheduling, thereby improving efficiency and reducing energy waste during transportation.

(2)

The market demand fluctuation indicator ranks second in weight and exhibits significant fluctuation in the curve, indicating that demand fluctuation has high uncertainty in its impact on supply chain stability. When selecting service providers, full consideration should be given to their logistics processing procedures, transportation methods and service scope; contracts should be signed to clarify the liability for compensation and specific measures in the event of goods damage or loss. Additionally, in the process of service provider screening and contract signing, the liability for compensation for demand fluctuation risks should be specified, and the compensation ratio should be linked to the demand fluctuation weight output by the model—when the weight exceeds the 15% threshold, the trigger threshold of the contract compensation clause shall be lowered by 20%. Furthermore, a “platform-based + localized” supply chain network should be constructed, and multi-model component sharing should be realized through modular design to reduce the impact of demand fluctuation on production.

(3)

Policy change is identified as the highest-priority risk factor by the model. The Hesitant Fuzzy DEMATEL algorithm assigns it a high basic weight based on expert evaluations, and the Entropy Weight method further verifies that policy adjustments will significantly affect data volatility, resulting in a high weight and substantial impact on supply chain risks. Based on this, a dedicated policy research team should be established to track real-time changes in policies such as carbon tariffs and environmental regulations at home and abroad, and formulate response strategies in advance. A policy compliance evaluation mechanism should be established to ensure that production processes and product standards comply with the latest regulatory requirements. In addition, the annual policy seminar mechanism should be strictly implemented, and the meeting agenda should be directly adjusted according to the policy change weight output by the model: if the weight increases by more than 5% month-on-month, one additional ad hoc meeting will be held in the next year; if the weight decreases for two consecutive years, the meeting frequency will be adjusted to once every two years.

4.5. Method Comparison and Analysis

To validate the robustness of the proposed HDEC algorithm, a comparative analysis was conducted between the HDEC algorithm and the traditional entropy-weighted AHP algorithm. The proposed HDEC algorithm avoids subjective bias and over-reliance on data during evaluation through a fusion of subjective and objective approaches. It also fully accounts for the hesitant fuzziness inherent in expert evaluations, thereby enabling accurate identification and assessment of risks within automotive parts supply chains. This study employs Pearson’s correlation coefficient and Spearman’s rank correlation coefficient to compare the weighting results of the proposed algorithm and the traditional entropy-weighted AHP from two complementary dimensions: “numerical magnitude” and “ordering logic.” This comparative analysis confirms the robustness of the HDEC algorithm.

The Entropy weight-AHP algorithm [30] was adopted to analyze and solve the risk factors and historical data in the case of this paper. The specific steps are as follows: 1. Construction of the risk factor index system. To avoid the impact of different index systems on the comparison of the two methods, the index system obtained by the fault tree analysis (FTA) and Delphi method in the previous section was used for evaluation; 2. Construction of a judgment matrix through pairwise comparison by experts, calculation of the eigenvector to obtain the AHP subjective weights, and completion of the consistency test; 3. Standardization of historical data and calculation of entropy weight objective weights by referring to the method in Section 4.2; 4. Fusion of subjective and objective weights using the linear weighting method, and finally obtaining the comprehensive weights and rankings of each index, as shown in Figure 7.

The indicators are sorted from top to bottom according to their weight values, with the numbers in the boxes representing the entropy-weighted AHP method weight values for each indicator. The standard deviation and covariance of the weights obtained from the HDEC algorithm and the entropy-weighted AHP method are calculated, respectively. Subsequently, the Pearson correlation coefficient between the two algorithms’ indicator weights is calculated as $r=0.8566$, and the Spearman correlation coefficient as $\rho =0.88$. It is demonstrated that the subjective-objective integrated evaluation algorithm based on symmetry thinking exhibits a strong correlation in weight values with traditional subjective-objective algorithms, complying with evaluation criteria and possessing high robustness. Moreover, building on traditional algorithms, this study fully considers the hesitant fuzziness of expert evaluations and the fluctuation characteristics of data, rendering the evaluation results more accurate and better aligned with practical applications. For example, the weight of the “transportation accident rate” indicator in the HDEC algorithm is 5 ranks higher than that in the entropy weight-AHP algorithm. The reason for this difference is that transportation accidents have strong chain destructive effects on the supply chain; once they occur, they are likely to trigger chain risks such as raw material supply disruptions and production plan stagnation. However, the traditional algorithm fails to consider the hesitant fuzziness of expert evaluations and the causal relationships between indicators, which tends to underestimate the risk priority of this indicator. This difference in ranking provides a more accurate priority orientation for supply chain risk management and makes up for the decision-making bias of traditional methods in ambiguous scenarios.

In summary, the subjective-objective comprehensive weighting method proposed in this paper, which is based on the hesitant fuzzy DEMATEL and entropy weight-coefficient of variation method, adopts three key technologies: first, decoupling differences in expert opinions through hesitant fuzzy sets to avoid subjective extreme errors; second, exploring the risk transmission logic by decoupling indicator correlations with DEMATEL; third, quantifying the information value and fluctuation characteristics of historical data by integrating the entropy weight method and coefficient of variation. In the “high-volatility, high-correlation, and high-ambiguity” risk assessment scenarios of the auto parts supply chain, the proposed method can make the indicator weights more consistent with the essence of risks and data laws, thereby providing scientific guidance for the risk management and optimization of the supply chain.

5. Conclusions

This study proposes a comprehensive research scheme for automotive supply chain risk assessment under the low-carbon context, aiming to address the deficiencies of existing traditional evaluation methods in terms of the comprehensiveness of risk factor identification, the hesitation of expert evaluations, and the consideration of data volatility. In the existing research on low-carbon automotive supply chain risk assessment, traditional methods generally suffer from incomplete coverage of risk factors, neglect of the uncertainty of expert judgments and the dynamic fluctuation characteristics of data, making it difficult to adapt to the complexity and multi-dimensionality of supply chain risks under low-carbon transition.

Firstly, the study determines the risk assessment index system through Fault Tree Analysis and the Delphi method, and then proposes the HDEC integrated evaluation model, which comprehensively considers index weights from both subjective and objective perspectives. Subsequently, taking the automotive parts supply chain system of a specific enterprise as an example, calculations are performed based on its data from 2019 to 2024 and expert evaluation data, identifying policy changes, market demand fluctuations, carbon emissions, production equipment efficiency, and transportation accident rate as key risk indicators, and proposing targeted response strategies accordingly.

Finally, the effectiveness of the model is verified through comparative experiments. Taking the traditional entropy weight-AHP algorithm as the benchmark, Pearson correlation coefficient and Spearman correlation coefficient are introduced to conduct robustness tests. The results confirm the significant advantages of the HDEC model in the accuracy and sensitivity of risk identification. This study not only improves the method system of supply chain risk assessment under the low-carbon context but also provides a scientific and feasible decision-making basis for supply chain risk management in the automotive industry during the low-carbon transition process.

Despite the progress achieved in the application of the HDEC algorithm for assessing automotive supply chain risks under the low-carbon context, this study still has the following limitations:

(1)

The limited application scenarios of the HDEC algorithm: The proposed integrated HDEC algorithm has strict requirements for the number of indicators, typically being applicable to scenarios with 5 to 15 indicators. When the number of indicators is excessively large, manual calculation becomes practically infeasible, and weight solving can only be performed via software—this increases the application threshold and renders the algorithm unsuitable for small-sample, low-resource research contexts.

(2)

Room for improvement in the quantitative accuracy of risk indicators: During the standardization of historical data for risk indicators, the quantitative calculation models designed for certain qualitative indicators are relatively simplistic with low sensitivity. These models fail to effectively reflect minor changes in risk indicators, potentially compromising the accuracy of objective weights.

(3)

Need for in-depth empirical validation: Although the rationality of the proposed algorithm in the context of automotive supply chain risk assessment has been verified through comparison with the traditional entropy weight-AHP method, multi-scenario and multi-method comparisons are lacking. Additionally, long-term tracking data have not been used to validate the practical application effects of dynamic decision-making.

To address the aforementioned limitations, future research can be further expanded in the following aspects:

(1)

Develop standardized calculation procedures: Integrate with tools such as Python 3.9 and MATLAB R2023b to develop standardized calculation codes, thereby reducing computational complexity. Simultaneously, expand the algorithm’s application scope in complex scenarios to enhance its usability.

(2)

Improve the mapping method for quantifying qualitative indicators: Design targeted quantitative calculation models based on the characteristics of different qualitative indicators. Clarify the accurate quantitative values corresponding to qualitative evaluations within specific ranges for each indicator, further improving the accuracy and logical rigor of objective weights.

(3)

Strengthen empirical research and cross-field expansion: Conduct long-term tracking of different types of supply chain enterprises, and verify the accuracy and superiority of the HDEC comprehensive algorithm through multi-method comparison. Extend the algorithm proposed in this paper to risk-sensitive fields such as the financial industry and the fire protection industry to test its cross-scenario applicability.