3.3.1. Introduction to Integrated Methodology
To effectively analyze the key factors and their interrelationships in the decarbonization of the construction supply chain, this study adopts an integrated analytical framework that combines Fuzzy-DEMATEL with Adversarial Interpretive Structural Modeling (AISM). This integrated method aims to overcome the limitations of traditional methods when addressing complex issues in the construction industry’s decarbonization. By combining fuzzy mathematics and adversarial learning, it not only reveals causal relationships between factors but also enhances the robustness and adaptability of the model in uncertain environments. The following sections elaborate on the applicability of these two methods in the field of construction decarbonization and explain the advantages of their combination:
The decarbonization of the construction supply chain involves the interaction of various factors across multiple dimensions, including policies, technologies, market demands, and social behaviors, all of which exhibit high uncertainty. In this context, Fuzzy-DEMATEL is particularly appropriate. Fuzzy-DEMATEL integrates fuzzy set theory [
37] with the Decision-Making Trial and Evaluation Laboratory (DEMATEL) method [
38] to effectively address the uncertainty and fuzziness of information. In the context of building decarbonization, Fuzzy-DEMATEL helps extract qualitative insights from expert judgments and converts these qualitative assessments into quantitative data through fuzzy processing, thus uncovering the causal relationships between key factors [
39].
For example, the relationship between low-carbon technologies and policies in the construction industry is fraught with uncertainty. Fuzzy-DEMATEL enables experts to assess uncertainties based on experience while minimizing human error [
40]. This feature makes Fuzzy-DEMATEL especially suitable for the field of building decarbonization, as it can reveal the complex interactions between policies, technologies, and market demands, accurately identifying the key drivers of decarbonization.
- 2.
The Applicability of AISM for Building Decarbonization Research
In contrast to Fuzzy-DEMATEL’s qualitative analysis strengths, AISM (Adversarial Interpretive Structural Modeling) enhances the dynamism and robustness of the analysis by introducing an adversarial learning mechanism. While traditional Interpretive Structural Modeling (ISM) methods can identify causal relationships, they have limited capability in handling hierarchical relationships and dynamic changes within complex systems [
38]. AISM, by simulating adversarial learning mechanisms [
41], allows the model to dynamically adjust based on data changes, thereby identifying more precise and refined causal relationships.
Specifically, for building decarbonization, AISM can adapt to the changing policy environment, technological advancements, and market demands. Through adversarial learning, it continuously optimizes model outcomes. For example, AISM can identify which policy measures are most influential in the decarbonization process and which technological innovations are the strongest drivers, providing more comprehensive and detailed decision support [
42]. This dynamic adjustment capability makes AISM an ideal choice for analyzing key factors and their hierarchical relationships in the building decarbonization process.
- 3.
The Advantages of Combining Fuzzy-DEMATEL and AISM
Although Fuzzy-DEMATEL and AISM each offer distinct advantages, their combination provides a stronger analytical capability. Fuzzy-DEMATEL offers a clear causal relationship framework, converting expert qualitative judgments into quantitative data while effectively managing uncertainty. AISM, on the other hand, further refines causal relationships and hierarchical structures through adversarial learning, enhancing the model’s adaptability to complex and dynamic environments.
By combining Fuzzy-DEMATEL and AISM, we can not only uncover the causal relationships among key factors in construction supply chain decarbonization but also dynamically adjust the model based on data changes, ensuring the efficiency and accuracy of the analysis [
43]. For example, in the decision-making process of building decarbonization, Fuzzy-DEMATEL provides an initial causal relationship framework, while AISM continuously optimizes this framework, making the interrelations between factors more precise and, therefore, providing more reliable decision support for policymakers and enterprises.
Furthermore, the combination of Fuzzy-DEMATEL and AISM offers additional advantages:
- (1)
Increased Transparency of Results: Fuzzy-DEMATEL clarifies causal relationships through fuzzy processing, while AISM further optimizes and adjusts, strengthening the robustness of the analysis results;
- (2)
Enhanced System Adaptability: The adversarial learning mechanism in AISM allows the model to optimize based on real-time data, which is crucial when dealing with dynamic factors such as policy changes and technological innovations in building decarbonization;
- (3)
Integration of Qualitative and Quantitative Analyses: Fuzzy-DEMATEL combines expert qualitative judgment with quantitative data, while AISM optimizes this combination through adversarial learning, ensuring high alignment between theoretical and practical applications of the analysis.
The Fuzzy-DEMATEL-AISM method provides a robust framework for analyzing factor hierarchies and causal relationships, offering critical insights into construction supply chain decarbonization. The methodological workflow is illustrated in
Figure 3, which highlights the key stages of the Fuzzy-DEMATEL and AISM analysis.
Stage 1: Initialization of the Impact Matrix
The process begins with the initialization of the impact matrix, where the relationships between various influencing factors are outlined. The arrow points to “Fuzzy Number Conversion”, indicating that the initial impact matrix is transformed into fuzzy numbers to facilitate further analysis.
Stage 2: Fuzzy Number Conversion
The initialized impact matrix is converted into fuzzy numbers, representing uncertainty and providing flexibility in the analysis. The arrow connects “Fuzzy Number Conversion” to “Defuzzification”, signifying the transition from fuzzy numbers to more precise data through defuzzification.
Stage 3: Defuzzification
In this stage, fuzzy numbers are defuzzified to produce crisp, precise values, which are then used for further analysis. The arrow points to “Normalization”, indicating that the defuzzified values undergo normalization to ensure consistency and comparability across factors.
Stage 4: Normalization
Normalization standardizes values to a common scale, ensuring that all factors can be effectively compared. The arrow connects “Normalization” to “Comprehensive Impact Matrix”, reflecting the final step where the normalized values are consolidated into a comprehensive matrix for causal analysis.
Stage 5: AISM Analysis
The comprehensive impact matrix is then used in AISM analysis to construct a hierarchical structure that illustrates the relationships between the factors. The arrow from “Comprehensive Impact Matrix” to “AISM Analysis” shows how the final matrix serves as the foundation for AISM model construction, providing valuable decision-making support for decarbonization strategies.
Each stage of the Fuzzy-DEMATEL-AISM method is interconnected, with the outputs of one stage providing the necessary input for the next, ensuring a systematic and logical progression of the analysis.
3.3.3. Expert Assessment of Influencing Factors
To ensure the accuracy and scientific validity of this study, a panel of 15 experts from the construction industry was invited to assess the identified influencing factors. The experts were selected based on the following key criteria:
Professional Background and Extensive Experience: The selected experts come from academia, industry, and policy-making sectors, with extensive experience and in-depth knowledge of decarbonization within the construction industry. This diversity ensures that the decarbonization influencing factors in the construction supply chain are assessed from multiple perspectives, thereby ensuring a comprehensive and accurate evaluation;
Industry Representation: The experts’ backgrounds span construction design, construction, supervision, engineering consulting, and academic research. This diverse range of expertise allows the expert panel to cover all aspects of the construction supply chain. The experts’ practical work experience provides an objective and comprehensive evaluation of the key factors and their interrelationships in the decarbonization process;
Rich Work Experience: The selected experts have work experience ranging from 5 to 15 years, as well as over 15 years, covering different career stages. This ensures both the comprehensiveness and depth of the evaluation. It also prevents bias by including experts with varying levels of experience, from highly experienced to moderately experienced;
Academic Background and Technical Expertise: Most of the experts hold doctoral degrees or higher, possessing strong theoretical and technical capabilities. This high level of academic training enables them to accurately understand the complex influencing factors of decarbonization and provide valuable insights during the assessment process;
Professional Title and Authority: The expert panel includes senior and associate senior professionals with significant authority in their respective fields. Their professional stature contributes to the authority and reliability of the evaluations provided for the study.
The detailed background information of the experts can be found in
Table 7. Based on this background, the experts conducted a professional assessment of the interrelationships between the influencing factors, according to the pre-established evaluation criteria (
Table 8). This expert evaluation ensures a comprehensive and scientifically rigorous analysis of the decarbonization factors in the construction supply chain.
The evaluation matrix was constructed as, where represents the degree of direct influence of factoron factor .
The criteria for scoring the impacts were as follows:
Expert opinions were obtained through face-to-face and telephone interviews to enhance the reliability and scientific rigor of the assessments. The collected data were processed using MATLAB R2023a and Python 3.12.0, ensuring consistency and accuracy. Key metrics, such as influence scores and centrality, were calculated to determine factor hierarchies, which served as the foundation for further analysis.
This thorough expert evaluation approach ensured that the collected data were of high quality, providing a robust basis for subsequent DEMATEL computations in
Section 3.3.6.
3.3.5. Defuzzification Using the C.F.C.S. Method
In this study, the C.F.C.S. (Converting Fuzzy Data into Crisp Scores) method [
44] was used to convert the fuzzy direct influence matrix into a clear, crisp form. This approach enhances the accuracy of factor analysis by reducing the influence of subjectivity while maintaining the integrity of the numerical data. The C.F.C.S. method calculates the upper and lower bounds for the scores using fuzzy minima and maxima. Subsequently, the total score is obtained by computing the weighted average of the membership functions, minimizing any loss of precision.
The specific steps are as follows:
, Standardization: The lower, middle, and upper bounds of the fuzzy numbers are normalized to facilitate comparability across different factors.
- 2.
Calculation of standardized values for the left and right sides:
- 3.
Calculation of the total standardized value:
- 4.
The defuzzification value for each expert’s evaluation denoted as
is then computed:
- 5.
Combining the evaluations of x experts yields the defuzzified direct impact matrix:
Defuzzification: Calculate a precise score for each factor by integrating expert evaluations into a unified matrix.
Several key factors influencing the decarbonization of the construction supply chain were identified, including F1, F2, F3, …, and F17 (see
Table 3). A scale of 0 to 5, ranging from “No impact” to “very high impact”, was used to quantify the interactions among these factors. Data on factor interactions, particularly the strength of their mutual influence, were collected through expert surveys.
This methodology ensured that the resulting matrix accurately captured the interrelationships within the construction supply chain. The data derived reflected the degree of influence and relevance of each factor in the actual construction supply chain context. While the study emphasized the relative strength of factor interactions, it did not distinguish the directional effects of these influences. To mitigate the potential bias, the arithmetic mean of expert evaluations was calculated, resulting in a precise initial direct influence matrix (as shown in
Figure 4).
3.3.6. DEMATEL-AISM Analysis
To further analyze the causal relationships among factors, the DEMATEL method was employed. The structured expert evaluation results (detailed in
Section 3.3.3) were converted into a direct-relation matrix, and MATLAB/Python tools were used to conduct DEMATEL calculations. These tools ensured high computational accuracy and allowed for the precise identification of key influencing factors.
Various methods exist for matrix normalization, and in this study, the row maximum method [
45] is applied. The directed topology map construction follows. This approach involves identifying the largest value within each row of the matrix
, Once the maximum value for a row is determined, all elements of the matrix
in that row are divided by this value. As a result, the standardized influence matrix
is constructed, ensuring the comparability of the matrix’s elements across rows.
- 2.
Integrated impact matrix.
The integrated system matrix captures the combined effects of the interactions among the different elements within the system.
where
is the unit matrix. This is shown in
Figure 6.
- 3.
The measures of influence degree, centrality, causality, and weight for each factor are systematically calculated.
- (1)
Degree of Influence: Influence Degree: Defined as the total impact of an individual element on all other elements; this measure is computed by summing the values of each row in the matrix
. Denoted as
, it quantifies the extent to which a specific element influences the system.
- (2)
Degree of Influence: This term refers to the sum of all columns in the matrix
, which indicates the total influence that the elements in each column exert on all other elements within the system. The value is represented as
.
- (3)
Centrality: Centrality reflects the importance and positional relevance of a factor within the evaluation system. This metric, denoted as
, is derived by aggregating the total influence exerted by an element and the combined influence it receives from all other elements. It provides a comprehensive measure of the role and significance of the element in the overall system.
- (4)
Degree of Causality: The causality degree of an element is obtained by calculating the difference between the total influence received from other elements and the influence it exerts on them. Represented as
, this value reflects the element’s net causative role in the evaluation framework.
Normalization and Weighting: The centrality values are then normalized, which allows the calculation of indicator weights. The outcomes of this process are presented in
Table 9.
In the Cartesian coordinate system, centrality is plotted along the horizontal axis, and causality is represented on the vertical axis. This graphical representation (see
Figure 7) provides a clearer understanding of each factor’s role in the low-carbon building supply chain and offers guidance for practical implementation.
Factors with high driving force and low dependence, such as F13 (low-carbon policy and regulatory guidance), F15 (low-carbon consumer preferences), and F16 (low-carbon advocacy by social organizations and media), are located in the upper-right quadrant. These factors are key drivers in the framework and play a crucial role in promoting the overall low-carbon transformation of the industry. For instance, F13 (low-carbon policy and regulatory guidance) provides the necessary regulatory framework and incentives to guide the market and industry towards low-carbon objectives. F15 (low-carbon consumer preferences) and F16 (low-carbon advocacy) help create market demand and societal support for low-carbon buildings by raising public awareness. Therefore, prioritizing interventions for these factors is crucial. Strengthening policy support, increasing consumer demand for low-carbon products, and expanding public participation through social advocacy will accelerate the decarbonization process and create a stable foundation for the transition.
On the other hand, factors with low driving force and high dependence, such as F2 (low-carbon equipment supply), F3 (low-carbon transportation), F7 (low-carbon structural design), F10 (low-carbon construction process), and F12 (low-carbon construction waste recycling), are located in the lower-left quadrant. These factors are highly influenced by external drivers, particularly government policies and market demand. In practice, management efforts should focus on stabilizing and strengthening the key drivers that influence these factors, such as F13 (policy) and F15 (consumer demand), to ensure the optimal outcomes of these dependent factors. For example, F7 (low-carbon structural design) and F3 (low-carbon transportation) should be optimized by reinforcing low-carbon technology policies and promoting green procurement in the market.
Factors in the autonomous quadrant, such as F1 (low-carbon energy and material supply), F4 (low-carbon supplier and contractor selection), F5 (low-carbon property management), F6 (low-carbon construction and operation concepts), and F11 (low-carbon information sharing), exhibit low driving force and low dependence, meaning that their impact on the overall system is limited. Although these factors are more independent, they may pose potential risks and instability in certain situations. Therefore, even though their direct impact on decarbonization is smaller, continuous monitoring is important to prevent potential disruptions caused by their independence.
In conclusion, the graphical analysis reveals the practical applications and intervention strategies for each factor. F13 and F15, identified as major drivers, should be prioritized for targeted intervention and policy support, while factors in the autonomous quadrant, such as F1 and F5, require regular monitoring to prevent potential risks from their independence and maintain overall system stability.
- 4.
Establishment of adjacency matrix.
To establish the adjacency matrix
, the internal relationships between influencing factors were determined through expert scoring. An evaluation method based on binary relations was applied, where
= 1 indicates a direct influence between factors, and
= 0 indicates no such influence, as shown in Equation (17).
The threshold value φ, φ
, is a critical parameter that determines the inclusion of relationships in the adjacency matrix. When sample data are limited, φ can be set to 0 based on expert judgment. In this study, the values were refined through multiple iterations, utilizing the mean
and standard deviation
of the integrated impact matrix to ensure the analysis adhered to rigorous scientific standards. Following this approach, the adjacency matrix
was established to represent the direct influence relationships between factors, as shown in
Table 10.
- 5.
Calculate the reachable matrix
The reachable matrix
was derived by iteratively multiplying the adjacency matrix
with the unit matrix
. The calculation continues until the matrix stabilizes, indicating no further changes, as described in Equation (18). The finalized reachable matrix
(
Table 10) reveals all possible paths between factors, indicating the degree of interconnection and dependency within the system.
The calculation of the reachable matrix
is formalized as follows:
The reachable matrix
is obtained from Equation (2) (
Table 11).
- 6.
Creating a general skeleton matrix
The reachable matrix
undergoes a “shrinking” process, where points forming loops are compressed into a single point. After this operation, the reachable matrix is updated to
. Subsequently, edge reduction is performed, which effectively eliminates redundant paths. The method for this operation is as follows:
The matrix
is subjected to edge reduction, resulting in a skeleton matrix
. By substituting loop elements, the generalized skeleton matrix
is obtained, as shown in
Table 12.
- 7.
Hierarchical Extraction
Using the reachability matrix, we calculate the prior set
, reachable set
, and the intersection set
(as shown in
Table 13). While the reachable and prior sets illustrate the relationships between elements, they do not directly reveal the hierarchical structure. Therefore, we need to divide the hierarchy by the relationship between these three. If the intersection set is equal to the reachable set, the element is the first layer factor (UP type); if the intersection set is equal to the prior set, it is the penultimate layer factor (DOWN type). After that, the stratified elements are deleted and the process is repeated until the stratification is completed.
Based on the data presented in the previous table, adversarial cascade extraction is conducted, and the resulting findings are shown in
Table 14.
- 8.
Mapping of Directed Topology Hierarchies
A directed topology map was constructed based on hierarchical relationships derived from the skeleton matrix and the hierarchical table. The UP-type hierarchy represents a bottom-up flow in which lower-level factors provide foundational support for upper-level factors. In contrast, the DOWN-type hierarchy represents a top-down flow, with higher-level factors exerting direct influence and providing feedback to foundational elements.
In this diagram:
Directed line segments represent the reachable relationships among factors;
Bi-directional arrows indicate loops that highlight mutual influence or feedback;
Lower-level factors indicate fundamental contributions, whereas upper-level factors exert direct effects. Intermediate factors exhibit mutual interdependence and serve transitional roles within the hierarchy.
Figure 8 illustrates the UP-type and DOWN-type directed topology diagrams, comprehensively visualizing hierarchical relationships and factor interdependencies. This graphical representation clarifies the structure and interactions of influencing factors, facilitating an understanding of complex systems such as construction supply chain decarbonization.