What Are the Obstacles to Promoting Photovoltaic Green Roofs in Existing Buildings? The Integrated Fuzzy DEMATEL-ISM-ANP Method

Abstract

Photovoltaic green roofs can contribute to energy conservation in buildings and the sustainable development of cities, but they have yet to be widely used due to many factors. Therefore, it is necessary to investigate the factors limiting the promotion of photovoltaic green roofs and to clarify their interactions. Based on the existing literature and expert recommendations, this paper summarizes 20 factors affecting its promotion. Fuzzy DEMATEL was used to analyze the causal relationship and importance of the influencing factors. A hierarchical structure was established using the interpretative structural model (ISM) to visually represent the layered structure and pathways of the factors. The role and status of each influencing factor were determined using the cross-influence matrix analysis method (MICMAC). Finally, the analytic network process (ANP) was combined with the overall influence matrix to determine the overall weight of each factor. Combined with the DEMATEL-ISM-ANP method, nine key influencing factors, namely, the lack of incentive policies, imperfect technical specifications and evaluation standard system, local economic development level, residents’ cognition, residents’ willingness, enterprises’ technical problems, the lack of relevant talents, the lack of capital investment, and cooperation mode, were finally identified and analyzed, and suggestions and strategies for improvement were proposed.

1. Introduction

The construction industry, one of China’s top three sectors in energy consumption and carbon emissions [1], accounted for 45.5% of the country’s total energy consumption and 51.6% of its carbon emissions in 2020 alone. In 2021, China’s total construction area will be approximately 67.7 billion square meters, making it the world’s largest construction market. In China, the rapid development of the construction industry has accelerated energy consumption, making energy conservation in buildings urgent. To better achieve the government’s “dual-carbon targets”, on the one hand, it is necessary to accelerate the development of green buildings, including zero-carbon buildings and photovoltaic building integration. On the other hand, it is necessary to carry out energy-saving renovations in existing buildings. According to the Ministry of Housing and Construction, in 2022, the proportion of new green building areas in China’s new buildings exceeded 90%, totaling 86,897,000 square meters. In the same year, the market size of the energy-saving renovation of existing buildings in China reached more than 1.5 trillion yuan, with a year-on-year growth of more than 10%, and the energy-saving renovation of buildings has shown great potential. Energy-saving roof renovation can improve the building’s energy utilization efficiency, reduce energy consumption, improve the indoor environment, and promote the development of green buildings. It is also essential to realize sustainable development and protect the environment. Current mainstream sustainable roofs include: green roofs, photovoltaic roofs, and cold roofs. Sustainable roofing can reduce energy consumption, improve the built environment’s quality, and positively impact the environment. Graziano et al. showed lower indoor temperatures for large green roofs compared to conventional cement tiles, with a difference between 6 and 8 degrees Celsius [2]. Lin et al. showed that using photovoltaic roofing in a building renovation project saves about 60% of the building’s energy consumption, which is economically feasible considering local energy tariff policies [3]. For commercial buildings, cool roofs can save 14–52% of the cooling load [4]. The combination of photovoltaic and green roofs is a new trend in the construction field, which provides additional benefits compared to single green and photovoltaic roofs, such as on-site power generation [5]. Photovoltaic green roofs are a promising alternative energy source because they have many benefits, including reducing carbon dioxide emissions [6], reducing energy consumption [7], conserving rainwater [8], improving biodiversity [9,10], and improving the power generation of photovoltaic systems [11]. When the surface of photovoltaic modules heats up due to solar radiation, the increase in ambient temperature harms their efficiency, performance, and reliability. However, combining green roofs (GRs) with photovoltaic (PV) systems helps to maximize the power output of PV systems through evaporative cooling [12,13]; meanwhile, the shielding effect of the solar panels can reduce the temperature of the ground below, thereby reducing indoor energy consumption [14]. Prakhar et al. demonstrated that photovoltaic green roofs provide energy savings under different climatic conditions [15]. Fernando et al. investigated the synergistic effect of photovoltaic panels and green roofs and verified the benefits of their combination [16]. Varuni Jayasooriya validated the financial feasibility of green and photovoltaic roofs through an investment payback period and net present value analysis [17]. Through probability analysis, Zhaozhi Wang et al. verified that the GR-PV system is a low-risk investment, resulting in a shorter payback period for energy and carbon emission investments [18]. From social and private perspectives, Francesco et al. developed a probabilistic cost–benefit analysis model for photovoltaic green roofs. They verified that photovoltaic green roofs can contribute to achieving several objectives of the European Green Deal [19]. From an economics and carbon emission perspective, Mehmet conducted a long-term, in-depth study of photovoltaic green roof installations. According to the sample application, the green roof application would become economic in about 7 years [20]. Valeria Todeschi et al. investigated the potential, feasibility, and impact of roof renovation in the Turin region. The study’s results supported the idea that integrating GR and PV systems can reduce energy consumption; reduce the urban heat island effect; and improve the environment, economy, and society [21].

Although photovoltaic green roofs are a promising technology, their application in China still needs to be improved, and research is still needed on their promotion and application. The promotion of photovoltaic green roofs faces many obstacles, but the mutual influence and relationship between these obstacles still need to be determined, and their importance remains unknown. Therefore, this study aims to systematically identify the main driving forces that influence the promotion of photovoltaic green roof renovation in existing buildings, investigate the causal relationship and hierarchical structure of these driving forces, and identify the mechanisms through which these forces interact. This study contributes to the existing literature in two ways. First, through literature review and expert evaluation, we systematically identify the factors that affect the promotion of photovoltaic green roof renovation in existing buildings. Second, the hybrid fuzzy decision experimental and evaluation laboratory (DEMATEL), the interpretive structural model (ISM), and the analytic network process (ANP) methods are used to analyze the interrelationships and impacts of the identified barriers. Specifically, (1) the fuzzy DEMATEL method is used to determine the significance of factors and quantify the causal relationship between these factors to determine the causal and outcome factors for promoting photovoltaic green roof renovation in existing buildings; (2) a multilevel recursive outcome model is established using the DEMATEL-ISM, revealing the complex mechanisms of action between different factors; (3) the ISM-MICMAC model is used to partition autonomous, dependent, correlated, and independent factors, clarifying the substantive role of factors in the system; (4) the DEMATEL and ANP methods are combined to obtain the mixed weights of each factor. The remainder of this study is divided into the following sections: Section 2 details the identification of contributing elements. Section 3 explains the process, while Section 4 presents the findings and analyses. Comprehensive analysis and discussion are provided in Section 5. The final portion contains the conclusions and prospects.

2. Construction of Restrictive Factor Indicator System

The factors affecting the promotion of photovoltaic green roof retrofits in existing buildings are diverse and complex. Although there is little direct research on this topic, we can still summarize various barriers from the relevant literature. After the preliminary compilation and summary of barriers, experts reviewed and identified 20 barriers divided into six categories, namely, macroeconomic policy factors, participant factors, capital cost factors, project factors, market factors, and social factors, as shown in

Table 1. Influencing factor indicators.

Dimension	Number	Factors
Macroeconomic policy factors	A1	Lack of incentive policies
	A2	Technical specifications, evaluation standards, and systems are not sound
	A3	Local economic development level
Participant factors	B1	Lack of coordination mechanism
	B2	Residents’ cognitive level
	B3	Residents’ willingness
	B4	Enterprise technical issues
	B5	Lack of relevant talents
Capital cost factors	C1	Lack of capital investment
	C2	Uncertainty in investment returns
	C3	Increased maintenance costs
Project factors	D1	Existing building measurement and evaluation measures
	D2	Lack of post-maintenance management
	D3	Difficulty and duration of the renovation
	D4	Environmental and nuisance issues after renovation
Market factors	E1	Inadequate supply chain and supporting infrastructure
	E2	Cooperation mode
	E3	Market entry threshold
Social factors	F1	Demographic characteristics
	F2	Lack of promotion platforms and activities

.

2.1. Macroeconomic Policy Factors

The macroeconomic situation and policy factors are crucial for the local photovoltaic green roof renovation, and they mainly include three factors: (1) Lack of incentive policies: Policy is a critical factor in promoting green renovation of buildings [22], and the lack of government promotion and incentive policies is considered the greatest obstacle to implementation [23]. Siwei Chen pointed out that in the vast majority of cities, the types of green roof incentive policies lack diversity [24], and the strategy of diversifying incentives is an essential factor for the success of China’s photovoltaic industry [25]. The effectiveness and sustainable implementation of policies are crucial for the development of green infrastructure, and such policies are applicable in both developed and developing countries [26,27]. Therefore, the lack of incentive policies also hinders the development of photovoltaic green roofs. Incentive policies mainly include providing funds (subsidies, grants, and kickbacks) to stakeholders. (2) Technical requirements, evaluation criteria, and methods: These aspects could be improved. Siwei Chen and Liming Bo both highlighted the lack of a complete rating system for green roofs and the problem of insufficient promotion and use of green buildings [24]. A significant factor is the lack of relevant green building ratings [28]. Establishing Chinese green building evaluation standards is necessary for the growth of Chinese architecture in terms of energy conservation [29]. One of the significant challenges hindering the development of photovoltaic green roofs is the lack of reliable technical specifications, evaluation criteria, and systems. (3) The level of local economic development: The level of regional economic development in China is uneven, and the tax revenue of a region determines the investment in the application of new technologies. At the same time, the strength of incentive policies is also related to the level of local fiscal revenue. The study by Kelly and Carolina suggests that developing photovoltaic green roofs requires significant economic policies to support future growth [30]. The level of photovoltaic green roof development in a region is closely related to the local economic development and productivity level. In areas with sound economic development, more sufficient funds are invested in supporting the photovoltaic green roof industry, technology updates, and supporting facility construction, which is conducive to developing photovoltaic green roofs in the region.

2.2. Participant Factors

The participant factors primarily involve the stakeholders in the project’s renovation and comprise five subfactors: (1) Lack of coordination mechanisms: Stakeholders (such as government, property owners, and enterprises) have different interests, and information asymmetry among them is an obstacle to the implementation of transformation policies [31]. When there are multiple owners of the roof, the difficulty of coordination among different entities increases. In the early stage of renovation, coordination among relevant units such as water and electricity, pipeline network, and telecommunications is required, which makes it difficult to unify the renovation cycle. (2) Residents’ cognitive level: Understanding residents’ attitudes and opinions about green infrastructure is crucial for promoting related technologies [32]. According to the study by Darko, the most significant barriers to green building have always been ignorance and resistance to technical progress [33]. C. Y. Jim’s research on green roof and green wall installation policies and Dutt and Dwarkeshwar’s research on rooftop solar energy policies indicate that raising residents’ awareness is an urgent task for their effective implementation [34,35]. (3) Residents’ willingness: This includes two main aspects, namely, their willingness to invest in photovoltaic green roofs and adopt the technology. The lack of motivation among homeowners and the high initial cost are two major obstacles to the development of green buildings [36], and photovoltaic green roofs face the same challenges. At the same time, the willingness to adopt new technologies could be higher due to low public awareness of energy efficiency [37], and the study by He Qing shows that political factors influence the willingness of residents to engage in green transformation [38]. The government should inform the public about this technology to increase their understanding of photovoltaic green roofs and energy literacy, and their willingness to make early investments [39]. (4) Enterprise technical issues: The technical difficulties in the design and construction process hinder the sustainable development of green roofs [40], which is also applicable to the development of photovoltaic green roofs, and technological progress is the fundamental driving force for industry development [36]. (5) Lack of relevant talents: The main obstacle to promoting green building renovation in China is the need for more organizations and expertise [41]. The level of photovoltaic green roof technology can only be improved with the joint efforts of the government, society, universities, research institutions, enterprises, and the public. The focus is on promoting the research and implementation of photovoltaic green roof technology and cultivating talents. Relevant departments should simultaneously promote the improvement in technical standards and specification evaluation systems.

2.3. Capital Cost Issues

The issue of capital cost is critical to the progress of a project and an essential prerequisite for renovation activities; it includes three factors: (1) Lack of capital investment: Hrovatin et al. pointed out that early investment in renovation activities is a crucial factor affecting building renovation [42], and the high initial cost is also a significant obstacle to the development of green buildings [36]. According to Chan et al., insufficient funding is among the top three significant barriers to advancing green building technologies [43]. Therefore, the lack of capital investment is also a key factor hindering its development for the photovoltaic green roof renovation of existing buildings. (2) Uncertainty of investment returns: Due to the high initial investment, the investment payback period for photovoltaic green roofs is longer, which may pose risks to renovation investors. Due to the complexity of buildings and the availability of technology, the performance of renovated buildings is still being determined, which directly affects the economic returns achieved [44] and leads to increased maintenance costs. Increased maintenance costs are considered one of the major barriers to implementing green roofs [22]. C. Y. Jim’s study suggests that Tokyo residents are aware of the long-term maintenance costs of green roofs [34]. Green roofs are associated with significant maintenance costs [45]. These costs include the ongoing maintenance related to planting, such as irrigation, fertilization, general cleaning, and insect management [46].

2.4. Project Factors

Project factors refer to the reasons for the project itself or the problems encountered during or after the implementation process, mainly including four aspects: (1) Existing building measurement and evaluation measures: Due to the multiple ownership of high-rise building roofs and the installation of many building services, the structural capacity of the building may need to be improved for the application of photovoltaic green roof systems. Therefore, an evaluation of the roof must be performed [23]. The service life of the building and the load it can withstand are all aspects that need to be evaluated. (2) Lack of post-maintenance management: Both photovoltaic systems and green plants need post-maintenance management to function better. After renovation, some residential areas may need a property management team, which makes it difficult to maintain the results of any later renovation. (3) The duration and difficulty of renovation: The duration of renovation, construction difficulty, and coordination difficulty will all affect a company’s contracting of a project. Construction difficulty includes a narrow site, tight schedule, and quality control; coordination difficulty includes construction noise and ventilation impact. (4) Environmental disturbance after renovation: Mosquitoes and plant waste are recognized as factors that have negative impacts on green roofs [34,47,48], and photovoltaic green roofs also face such problems.

2.5. Market Factors

The interaction of comprehensive social and environmental factors plays a role in the development of the green roof market. The formation of the photovoltaic green roof market cannot be separated from the joint effects of social culture, industrial chain, supporting institutions, and market norms. The market factors mainly include three aspects: (1) The industrial chain and supporting facilities: The strategies involving these aspects must be sound. Improving the industrial chain and supporting facilities requires, on the one hand, the development of photovoltaic green roofs to bring tangible economic and social benefits. On the other hand, the government must increase its support. The government needs to “foot the bill” first in the early stage. When the industrial chain is completed and can bring benefits, the government can appropriately recover the cost. (2) Cooperation mode: The cooperation mode refers to how the funds of social capital are invested in the transformation, how the benefits are obtained, and how the social capital intersects or binds with the owners’ interests during the transformation. Cooperation modes include BOT, PPP, and so on. (3) Market entry threshold: This threshold refers to the social forces that can participate in renovating existing buildings’ photovoltaic green roofs. The government favors enterprises that use state-owned assets, is skeptical about private and small enterprises, and is concerned about whether they can responsibly complete the renovation work. Therefore, a market entry threshold will be set to evaluate enterprises’ ability.

2.6. Social Factors

The social factors for the promotion of photovoltaic green roofs in existing buildings include two main aspects: (1) Demographic characteristics: These include gender, age, monthly family income, education level, and employment. According to previous research, those who have attained a high level of education generally have a more favorable attitude toward urban green spaces [49]. A previous study in the Northeastern United States confirmed that age and education are factors that influence general attitudes toward green roofs [50]. Brigglio Marie et al. found that, among the key factors associated with the acceptability of photovoltaic systems, younger families tend to adopt these systems more easily [51]. Educational level, perceived value, and perceived behavioral control are directly proportional to attitudes toward green transformation and willingness to pay [52]. (2) Lack of promotional platforms and activities: Lack of platforms (such as media, applications, and networks) and activities dedicated to promoting photovoltaic green roofs should also be considered.

3. Methodology

3.1. Research Framework

The decision experimental and evaluation laboratory (DEMATEL) technique is a comprehensive approach that integrates graph theory and matrix theory to effectively study and make informed judgments about complicated system elements [53]. This method thoroughly identifies and analyzes factors within complicated networks [54]. The DEMATEL method is highly effective for identifying causal relationships between assessment parameters and revealing structural patterns [55,56]. This method considers the interdependence between variables and clusters of alternative solutions in large systems with many failure modes [57]. Individual variations and expert subjectivity strongly influence the conclusions of the DEMATEL method since it relies on expert knowledge to determine the scoring, which may lead to biases and misinterpretations of relationships. Therefore, the integration of fuzzy theory with the DEMATEL approach is considered essential to address the challenges associated with inaccuracies and biases arising from expert assessment data [58]. The interpretive structural model (ISM), a well-known network analysis tool based on graph theory, processes and analyzes complex system structures using logical matrix operations. In recent years, ISM has become an effective tool for system analysis. Based on expert experience and knowledge mining, it can decompose disordered elements in complex systems into multilevel hierarchical structural models [59,60]. In order to properly evaluate the main components, influence the degree of the indicator system, and build the hierarchical relationship of the indicator system, the DEMATEL and ISM methods need to be combined [61]. Meanwhile, the combination of the two can reduce the computational complexity and the complexity of the accessible matrices in the ISM. The MICMAC approach focuses on analyzing the magnitude of the driving and dependent forces of each factor in the system, with the primary objective of identifying the key factors that significantly influence the system, and is the final step in conducting an ISM analysis [62,63]. The use of the DEMATEL and ISM approaches allows for a more comprehensive representation of the causal relationships between different components within the system, including their order, direction, and hierarchy. However, the determination of weights remains an intractable task. Therefore, incorporating the analytic network process (ANP) to determine priority weights for systems with dependency and feedback relationships also overcomes the shortcomings of the ANP. In addition, because all starting element weights in the ANP calculation results are 0, to avoid this phenomenon, the total influence matrix is combined with the weight vector of the ANP method to obtain a mixed weight. Therefore, the integration of the DEMATEL-ISM-ANP method in this article can effectively and systematically describe the interrelationships between the restrictive factors for promoting photovoltaic green roof renovation in existing buildings, establish a hierarchical structure model for photovoltaic green roof renovation in existing buildings, and determine the weights of each factor. The flowchart is shown in Figure 1.

3.2. Research Methods

3.2.1. Triangular Fuzzy Number

To mitigate the inherent subjectivity associated with expert scoring, the use of fuzzy set theory and triangular fuzzy number (TFN) is proposed to quantify the assessment outcomes of experts employing linguistic factors [64,65]. Triangular fuzzy numbers are employed to leverage their inherent simplicity and computational convenience, enabling a more thorough depiction of the real-world scenario under consideration. By representing subjective assessments as a range rather than a singular precise value, triangular fuzzy numbers offer a means of capturing the nuanced nature of the problem at hand [66]. Let ω be the fuzzy number (TFN) on R, and triangular fuzzy numbers can be defined as triplets (l, m, n). The member function ω(x) defines the member level of an element as follows:

$$\omega \left(x\right)=\left\{\begin{array}{c}0,x\le l\\ \frac{m - x}{m - l},l\le x\le n\\ \begin{array}{c}\frac{n - x}{n - m},m\le x\le n,\\ 0,x\ge n\end{array}\end{array}\right.$$

(1)

3.2.2. Fuzzy DEMATEL-ISM-ANP Process

The model using the integrated fuzzy DEMATEL-ISM-ANP method is generated as follows:

Step 1: The influence of the factor indicator system was determined through a comprehensive literature review, and ten experts involved in the photovoltaic industry, green roof construction, and the renovation of old residential areas were invited to improve the list of influential factors. This aimed to eliminate unnecessary obstacles and merge similar and related obstacles.

Step 2: During this phase, researchers sought the participation of experts from both academic institutions and industry to employ the Delphi technique for the purpose of scoring and constructing a direct effect matrix. Triangular fuzzy numbers were used to represent five language phrases, and afterward, specialists were requested to examine the interconnections among each difficulty. The survey instrument utilizes a five-point Likert scale, and the semantic transformation table is presented in

Table 2. Semantic transformation table.

Language Operator	Triangular Fuzzy Number (TFN)
No impact (0)	(0, 0, 0.25)
Low impact (1)	(0, 0.25, 0.25)
Has a certain impact (2)	(0.25, 0.5, 0.75)
Has a high impact (3)	(0.5, 0.75,1)
Has a very significant impact (4)	(0.75, 1, 1)

.

Step 3: The initial direct impact matrix is converted into an initial direct relationship fuzzy matrix through the semantic table (see Table 1), ${\omega }_{ij}^k=(l_{ij}^k,m_{ij}^k,n_{ij}^k)$, where ${\omega }_{ij}^k$ means the degree to which the k-th expert believes that factor i affects factor j.

Step 4: A clear, direct impact matrix is built.

First, the centroid method of defuzzification is used to convert the triangular fuzzy evaluation into clear values according to Equation (2), assuming that Q is the cleaning value obtained after the centroid method of defuzzification calculation.

Q = [(m − l) + (n − l)]/3 + m

(2)

Then, the clear values of K respondents are aggregated, and the arithmetic mean is determined to obtain the average direct impact matrix $\overline{D}$.

$$\begin{gathered} \overline{{\omega }_{ij}^k}=1/k({\omega }_{ij}^1+{\omega }_{ij}^2+\cdots +{\omega }_{ij}^k) \\ \overline{D}=\left[\begin{array}{ccc}\overline{{\omega }_{11}^k}& \cdots & \overline{{\omega }_{1n}^k}\\ ⋮& \ddots & ⋮\\ \overline{{\omega }_{n1}^k}& \cdots & \overline{{\omega }_{nn}^k}\end{array}\right] \end{gathered}$$

(3)

Step 5: The comprehensive impact matrix is calculated.

Firstly, the average direct impact matrix is standardized using Equation (4) as follows:

$$N=\overline{D}/\underset{1\le i\le n}{max}{\sum }_{j=1}^n{\omega }_{ij}$$

(4)

Then, the comprehensive impact matrix is calculated using Equation (5), where E is the identity matrix.

$$\begin{gathered} {T=N(E-N)}^{-1} \\ T=\left[\begin{array}{ccc}{t}_{11}& \cdots & t_{1n}\\ ⋮& \ddots & ⋮\\ t_{n1}& \cdots & t_{nn}\end{array}\right] \end{gathered}$$

(5)

Step 6: The comprehensive impact matrix T is analyzed. The degree of influence F_i and the degree of influence G_i are calculated using Equations (6) and (7). These degrees of influence represent the comprehensive impact values of the i-th row or i-th column influencing factors on other factors.

$$F_i={\sum }_{j=1}^n{t}_{ij},i=\mathrm{1,2},\cdots ,n$$

(6)

$$G_i={\sum }_{i=1}^n{t}_{ij},i=\mathrm{1,2},\cdots ,n$$

(7)

The central degree $m_i$ reflects the position of the i-th factor in the indicator system and its importance in the failure process. The causal degree $n_i$ reflects the causal relationship of the influencing factor. The difference between the degree of influence and the degree of influence of an element k($n_i$) is called the cause degree of the element; if it is positive, it means that element k has a great influence on the other elements, which is called the cause factor; by contrast, if it is negative, it means that element k has a great influence on the other elements, which is called the result factor [66,67]. Centrality represents causation, and the formula is as follows:

$$m_i=F_i+G_i,i=\mathrm{1,2},\cdots ,n$$

(8)

$$n_i=F_i-G_i,j=\mathrm{1,2},\cdots ,n$$

(9)

Step 7: The overall impact matrix is calculated.

$$\begin{gathered} H = T + E \\ H=\left[\begin{array}{ccc}{h}_{11}& \cdots & h_{1n}\\ ⋮& \ddots & ⋮\\ h_{n1}& \cdots & h_{nn}\end{array}\right] \end{gathered}$$

(10)

Step 8: The threshold is set, and the reachability matrix is calculated.

Based on the comprehensive impact matrix T to construct the adjacency matrix U, experts need to define a threshold to eliminate the less influential factors in T. Thus, λ is the threshold, and the value range is in the range of [0, 1]. The value will directly affect the formation of the reachability matrix, thereby further affecting the hierarchical structure formed by the ISM. The adjacency matrix U is calculated based on the comprehensive influence matrix T using the formula below, where u_ij is the correlation value between factor i and element j.

$$\begin{gathered} u_{ij}\left\{\begin{array}{c}1\hspace{1em}{h}_{ij}\ge \lambda \left(i has a direct impact on j\right)\\ 0\hspace{1em}{h}_{ij}<\lambda \left(i has no direct impact on j\right)\end{array}\right.,j=\mathrm{1,2},\cdots ,n \\ U=\left[\begin{array}{ccc}{u}_{11}& \cdots & u_{1n}\\ ⋮& \ddots & ⋮\\ u_{n1}& \cdots & u_{nn}\end{array}\right] \end{gathered}$$

(11)

Reachable matrices belong to Boolean matrices, which are operated on using the sum of identity matrix E and adjacency matrix U, E + U, according to Boolean operation rules, namely, (0 + 0 = 0; 0 + 1 = 1; 1 + 1 = 1; 1 × 0 = 0; 0 × 1 = 0; 1 × 1 = 1), until the formula $K={(U+E)}^{n+1}={(U+E)}^n\ne {\left(U+E\right)}^{n-1}\ne U+E$ is satisfied, and the reachable matrix K is finally obtained.

$$K=\left[\begin{array}{ccc}{k}_{11}& \cdots & k_{1n}\\ ⋮& \ddots & ⋮\\ k_{1n}& \cdots & k_{nn}\end{array}\right]$$

Step 9: The reachable set R(s_i) and the antecedent set A(s_i) of each influencing factor are calculated.

$$R\left(s_i\right)=\{s_j\in S|k_{ji}=1\}$$

(12)

$$A\left(s_i\right)=\{s_j\in S|k_{ij}=1\}$$

(13)

The elements of all columns in K in which the element value of row i is 1, where $k_{ij}$ is the element of row i and column j in K, constitute the reachability set $R\left(s_i\right)$. All row elements in K with column i element values of 1 are included in the preceding set $A\left(s_i\right)$, where $k_{ij}$ is the element in row j and column i.

Step 10: An ISM is established.

$$R\left(s_i\right)=R\left(s_i\right)\cap A\left(s_i\right)$$

(14)

where $R\left(s_i\right)$ is considered the initial level when Equation (14) is established; $R\left(s_i\right)$ is then subtracted from K, and the second level is calculated using Equations (12) and (14), etc., until the final level is calculated. The above-mentioned factor set may be used to create the ISM of affecting factors.

Step 11: With the MICMAC method, the driving force and dependent force of all factors are determined. Using the reachability matrix and MICMAC method, the driving force and dependence are calculated with Equations (15) and (16), where $k_{ij}$ is the element in the reachable matrix K.

$$\mathrm{Driving}\mathrm{force}:D_i={\sum }_{j=1}^n{k}_{ij}$$

(15)

$$\mathrm{Dependence}\mathrm{force}:R_i={\sum }_{i=1}^n{k}_{ij}$$

(16)

Then, a classification diagram of influencing factors is drawn based on the results of the driving force and dependence force. According to $D_i,R_i$ the influencing factors for the promotion of photovoltaic green roofs in existing buildings are divided into a self-cluster, an independent cluster, a dependent cluster, and a linkage cluster.

Step 12: An ANP network model is established.

The reachability matrix K is transformed into an ANP network structure, and the network model is established in the relevant software. The hierarchical relationships established with the ISM are used as structural inputs to the ANP model, and the macroeconomic policy factors, participant factors, capital cost factors, project factors, market factors, and social factors are used as “clusters”. Then, the next level of each indicator is used as a “node” within the cluster. “The structure of the ANP network is obtained.

Step 13: The unweighted supermatrix is determined.

Let the control layer elements in the ANP network structure be $v_1$,$v_2$,$v_3$,$\cdots$,$v_n$, and the network layer elements be $S_1$,$S_2$,$\cdots$,$S_n$, where $S_i$ contains elements $s_{i1},s_{i2},\cdots ,s_{in}$, i = 1,2,$\cdots$, n. Taking the control layer element $v_f$ (f = 1,2,$\cdots$, n) and the network layer element $s_{ij}$ (j = 1,2,$\cdots$, n) as the criteria, the 1~9 scale method is used to compare the elements. According to the comparison results, the judgment matrix is obtained. Then, the weight vector ($W_{i1}^{jk},W_{i2}^{jk},\cdots ,W_{in}^{jk}$)^T is calculated using the eigenvalue method. When k takes different values, the matrix $W_{ij}$ is obtained using the same principle.

$$W_{ij}=\left[\begin{array}{ccc}\begin{array}{cc}{W}_{i1}^{\left(j1\right)}& W_{i1}^{\left(j2\right)}\\ W_{i2}^{\left(j1\right)}& W_{i2}^{\left(j2\right)}\end{array}& \cdots & \begin{array}{c}{W}_{i1}^{\left(j{n}_j\right)}\\ W_{i2}^{\left(j{n}_j\right)}\end{array}\\ ⋮⋮& \ddots & ⋮\\ \begin{array}{cc}{W}_{i{n}_j}^{\left(j1\right)}& W_{i{n}_j}^{\left(j2\right)}\end{array}& \cdots & W_{i{n}_j}^{\left(j{n}_j\right)}\end{array}\right]$$

(17)

The sorting vector reflects the influence of the column vector $S_i$ elements in the matrix, $s_{i1},s_{i2},\cdots ,s_{in}$, on the elements $S_{j1},S_{j2},\cdots ,S_{jn}$ in the element $S_j$. When the elements in $S_i$ have no effect on the elements in $S_j$, $W_{ij}=0$. When i and j take different values, we can obtain the supermatrix $W_f$ using the criterion $v_f$ in the same way.

$$W_f=\begin{array}{c}{S}_1\\ \begin{array}{c}{S}_2\\ ⋮\end{array}\\ S_n\end{array}\left[\begin{array}{ccc}\begin{array}{cc}{W}_{11}& W_{12}\\ W_{21}& W_{22}\end{array}& \cdots & \begin{array}{c}{W}_{1n}\\ W_{2n}\end{array}\\ ⋮⋮& \ddots & ⋮\\ \begin{array}{cc}{W}_{n1}& W_{n2}\end{array}& \cdots & W_{nn}\end{array}\right]$$

(18)

Step 14: The weighted supermatrix is determined.

Taking each indicator element group as the criterion, the judgment matrix is further constructed, and the elements in each criterion are compared and normalized to obtain the normalized eigenvector ${[q_{1j},q_{2j},\cdots ,q_{nj}]}^T$. A consistency test is then conducted to assess its reliability, and the weighted matrix Q is determined as follows:

$$Q=\left[\begin{array}{ccc}\begin{array}{cc}{q}_{11}& q_{12}\\ q_{21}& q_{22}\end{array}& \cdots & \begin{array}{c}{q}_{1n}\\ q_{2n}\end{array}\\ ⋮& \ddots & ⋮\\ \begin{array}{cc}{q}_{n1}& q_{n2}\end{array}& \cdots & q_{nn}\end{array}\right]$$

(19)

The weighted supermatrix $\overline{W}$ is obtained by weighting the elements of the supermatrix.

$$\overline{W}=Q{W}_f$$

(20)

Step 15: The limit hypermatrix is calculated.

The weighted supermatrix $\overline{W}$ is stabilized; that is, the weighted supermatrix is calculated. The weighted supermatrix is obtained by calculating its limit relative weight.

$${\overline{W}}^{\infty }=\underset{k\to \infty }{\lim }{\left(\overline{W}\right)}^k$$

(21)

If the unique limit of convergence is obtained, the value of line I in the limit matrix is the subjective weight of the evaluation index of that line. Its weight is set as W, which is determined as $W={(w_1,w_2,\cdots ,w_n)}^T$.

Step 16: The mixed weight value of the factor is determined.

The mixed weight vector of the system is obtained according to Formula (22), and the mixed weight value of each factor is obtained. In this equation, Z is the vector of factors, $Z=(q_1,q_2,\cdots ,q_n)$, H is the overall influence matrix in Step 6, and W is the weight set vector.

Z = W + HW

(22)

Step 17: Final weights are determined.

The final weight ${\lambda }_i(i=\mathrm{1,2},\cdots ,n)$ of each influencing factor can be obtained by standardizing the mixed weight Z.

$${\lambda }_i=Z_i/{\sum }_{i=1}^n{Z}_i$$

(23)

4. Results and Analysis

4.1. Analysis of Fuzzy DEMATEL Results

In a study on the relationship between group size and decision making, it was noted that with a focus on quality congruence, 5 to 10 people are most appropriate [68]. In addition, using the investigator triangulation method and data from teams with different research members can reduce bias and ensure the effectiveness and reliability of the study [69]. Based on this, in this article, eight experienced experts in photovoltaic and green roofs were invited, comprising four from academic researchers and four from company personnel. An index system was developed to evaluate the influencing variables of photovoltaic green roofs in existing structures. The eight experts were involved in assigning values to the degree of interaction between these elements based on the five levels outlined in Table 2. Then, in Steps 3 and 4, the centroid approach was used to address the fuzziness issue. As a result, the eight processed direct impact matrices were averaged, deriving the average direct impact matrix, which is provided in

Table 3. Average direct impact matrix.

	A1	A2	A3	B1	B2	B3	B4	B5	C1	C2	C3	D1	D2	D3	D4	E1	E2	E3	F1	F2
A1	0	0.1458125	0.0833	0.124975	0.1458125	0.87495	0.1979	0.1458125	0.1979	0.0833	0.0833	0.1979	0.1458125	0.0833	0.0833	0.156225	0.0833	0.0833	0.0833	0.87495
A2	0.1041375	0	0.0833	0.1979	0.0833	0.0833	0.2708	0.0833	0.1041375	0.1041375	0.0833	0.87495	0.0833	0.0833	0.0833	0.0833	0.0833	0.9166	0.0833	0.0833
A3	0.9166	0.895775	0	0.1979	0.124975	0.1874875	0.1458125	0.572875	0.1979	0.124975	0.0833	0.16665	0.0833	0.0833	0.0833	0.87495	0.0833	0.0833	0.87495	0.1458125
B1	0.0833	0.0833	0.1041375	0	0.0833	0.0833	0.0833	0.0833	0.1041375	0.0833	0.0833	0.0833	0.87495	0.87495	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833
B2	0.0833	0.0833	0.0833	0.0833	0	0.854125	0.0833	0.0833	0.1041375	0.0833	0.0833	0.0833	0.1041375	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833
B3	0.0833	0.0833	0.0833	0.0833	0.0833	0	0.0833	0.0833	0.87495	0.0833	0.0833	0.1041375	0.0833	0.0833	0.0833	0.0833	0.1041375	0.0833	0.0833	0.0833
B4	0.0833	0.0833	0.22915	0.0833	0.0833	0.0833	0	0.1041375	0.1041375	0.895775	0.8333	0.2499875	0.124975	0.854125	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833
B5	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.9166	0	0.0833	0.0833	0.0833	0.16665	0.8333	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833
C1	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.1041375	0.0833	0	0.0833	0.0833	0.239575	0.1874875	0.895775	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833
C2	0.0833	0.0833	0.0833	0.0833	0.0833	0.87495	0.0833	0.0833	0.2187375	0	0.0833	0.0833	0.124975	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833
C3	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.1041375	0	0.0833	0.0833	0.0833	0.895775	0.0833	0.0833	0.0833	0.0833	0.0833
D1	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.124975	0.0833	0.0833	0	0.0833	0.895775	0.0833	0.0833	0.1770625	0.0833	0.0833	0.0833
D2	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0	0.0833	0.9166	0.0833	0.0833	0.0833	0.0833	0.0833
D3	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.1979	0.124975	0.0833	0.0833	0	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833
D4	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0	0.0833	0.0833	0.0833	0.0833	0.0833
E1	0.0833	0.0833	0.0833	0.1041375	0.0833	0.0833	0.0833	0.0833	0.1979	0.1041375	0.854125	0.0833	0.0833	0.87495	0.0833	0	0.0833	0.0833	0.0833	0.0833
E2	0.0833	0.895775	0.0833	0.2187375	0.0833	0.0833	0.0833	0.0833	0.270825	0.1458125	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0	0.895775	0.0833	0.0833
E3	0.0833	0.0833	0.0833	0.0833	0.87495	0.0833	0.0833	0.0833	0.1041375	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.124975	0	0.0833	0.0833
F1	0.0833	0.0833	0.0833	0.0833	0.9166	0.1979	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0	0.0833
F2	0.0833	0.0833	0.0833	0.0833	0.87495	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0.0833	0

. The normalization process was then performed up to Step 5, resulting in the acquisition of the complete impact matrix, which is visually presented in

Table 4. Comprehensive impact matrix.

	A1	A2	A3	B1	B2	B3	B4	B5	C1	C2	C3	D1	D2	D3	D4	E1	E2	E3	F1	F2
A1	0.022	0.05	0.032	0.04	0.074	0.181	0.059	0.044	0.079	0.041	0.045	0.062	0.055	0.069	0.044	0.047	0.033	0.042	0.035	0.166
A2	0.038	0.025	0.031	0.051	0.063	0.05	0.067	0.033	0.046	0.045	0.043	0.169	0.043	0.079	0.041	0.034	0.034	0.176	0.034	0.035
A3	0.185	0.188	0.03	0.068	0.095	0.107	0.079	0.127	0.087	0.063	0.075	0.091	0.071	0.108	0.061	0.179	0.044	0.073	0.177	0.076
B1	0.032	0.036	0.032	0.016	0.041	0.043	0.034	0.03	0.041	0.036	0.037	0.036	0.167	0.18	0.055	0.032	0.028	0.036	0.032	0.032
B2	0.028	0.032	0.025	0.026	0.023	0.164	0.03	0.027	0.053	0.03	0.032	0.033	0.036	0.047	0.034	0.028	0.026	0.032	0.028	0.028
B3	0.028	0.032	0.025	0.027	0.037	0.024	0.031	0.027	0.164	0.031	0.033	0.039	0.035	0.063	0.034	0.028	0.029	0.033	0.028	0.029
B4	0.04	0.045	0.057	0.035	0.049	0.069	0.027	0.041	0.054	0.176	0.167	0.071	0.052	0.191	0.062	0.04	0.034	0.043	0.04	0.038
B5	0.034	0.038	0.033	0.031	0.044	0.047	0.173	0.019	0.041	0.055	0.055	0.055	0.163	0.073	0.059	0.034	0.03	0.038	0.033	0.034
C1	0.029	0.033	0.026	0.027	0.038	0.039	0.034	0.028	0.021	0.034	0.035	0.058	0.051	0.183	0.037	0.029	0.027	0.033	0.029	0.029
C2	0.029	0.032	0.026	0.027	0.038	0.169	0.031	0.028	0.073	0.017	0.033	0.034	0.041	0.051	0.035	0.029	0.026	0.033	0.029	0.029
C3	0.028	0.031	0.025	0.026	0.036	0.038	0.03	0.026	0.033	0.033	0.018	0.031	0.032	0.044	0.166	0.028	0.025	0.032	0.027	0.028
D1	0.028	0.034	0.026	0.027	0.037	0.039	0.03	0.027	0.041	0.033	0.033	0.019	0.033	0.179	0.034	0.028	0.041	0.035	0.028	0.029
D2	0.028	0.031	0.025	0.026	0.036	0.037	0.03	0.026	0.033	0.03	0.032	0.031	0.018	0.044	0.17	0.028	0.025	0.032	0.027	0.028
D3	0.025	0.028	0.022	0.023	0.033	0.036	0.027	0.024	0.03	0.046	0.035	0.028	0.029	0.026	0.031	0.025	0.023	0.029	0.025	0.025
D4	0.024	0.027	0.022	0.023	0.032	0.033	0.026	0.023	0.029	0.026	0.028	0.027	0.028	0.038	0.015	0.024	0.022	0.028	0.024	0.025
E1	0.032	0.036	0.029	0.033	0.042	0.044	0.034	0.031	0.057	0.041	0.164	0.036	0.038	0.183	0.055	0.018	0.029	0.037	0.032	0.032
E2	0.035	0.172	0.031	0.057	0.065	0.051	0.041	0.033	0.074	0.049	0.04	0.058	0.044	0.065	0.042	0.035	0.019	0.192	0.034	0.035
E3	0.028	0.033	0.025	0.027	0.167	0.055	0.03	0.027	0.04	0.03	0.032	0.032	0.034	0.046	0.034	0.028	0.032	0.02	0.028	0.029
F1	0.029	0.032	0.026	0.027	0.174	0.075	0.031	0.027	0.039	0.031	0.033	0.033	0.034	0.046	0.034	0.029	0.026	0.033	0.015	0.029
F2	0.028	0.031	0.025	0.026	0.166	0.054	0.03	0.027	0.036	0.03	0.032	0.032	0.033	0.044	0.033	0.028	0.025	0.032	0.028	0.014

.

In Step 6, Equations (6) and (7) were used to calculate the impact, influence, centrality, and cause values of barriers to promoting photovoltaic green roof renovation in existing buildings, as shown in

Table 5. DEMATEL calculation index values.

Factor	Impact Degree D Value	Affected Degree C Value	Centricity D + C Value	Cause Degree D − C Value
A1	1.22	0.749	1.969	0.472
A2	1.135	0.968	2.103	0.168
A3	1.986	0.575	2.561	1.412
B1	0.975	0.645	1.62	0.331
B2	0.764	1.29	2.054	−0.527
B3	0.777	1.355	2.132	−0.578
B4	1.334	0.874	2.208	0.46
B5	1.088	0.676	1.765	0.412
C1	0.82	1.07	1.89	−0.249
C2	0.811	0.877	1.687	−0.066
C3	0.736	1.001	1.737	−0.266
D1	0.782	0.975	1.757	−0.193
D2	0.735	1.037	1.772	−0.303
D3	0.57	1.758	2.328	−1.188
D4	0.523	1.076	1.6	−0.553
E1	1.001	0.752	1.753	0.249
E2	1.173	0.576	1.749	0.596
E3	0.777	1.009	1.787	−0.232
F1	0.802	0.731	1.533	0.071
F2	0.756	0.77	1.526	−0.014

. In the causal degree dimension, the larger the value, the easier it is for that factor to influence other factors. Factors with a degree greater than 0 are causal factors, while those with less than 0 are outcome factors. According to Table 5, 9 causal factors and 11 outcome factors constrain the promotion of photovoltaic green roof renovation in existing buildings. The top five factors in the causal ranking are A3, E2, A1, B4, and B5, indicating that these five factors have the most significant impact on other factors and result in a greater difficulty of change. The five factors with the highest absolute values are D3, B3, D4, B2, and D2, indicating that these factors are most susceptible to other factors. The causal factor is usually an indirect factor affecting the promotion, while the outcome factor is a direct one.

Based on centrality and causality, the causal relationship was determined between the restrictive factors for promoting photovoltaic green roof renovation in existing buildings, as shown in Figure 2. Based on the results in Figure 2, the constraints on promoting photovoltaic green roof renovation in existing buildings are grouped into four categories. The first category is the strong causal factor set (Zone I), which impacts the facilitation of constraints related to photovoltaic green roofs and has a notable effect on other variables related to outcomes. The second category is the weak cause factor set (Zone II), which also exerts a notable influence on the facilitation of restrictions related to photovoltaic green roofs and other factors related to outcomes. The third category is referred to as the weak outcome factor set (Zone III), which results from the combined influence of many causal variables and exerts a discernible influence on the limitations facing photovoltaic green roofs regarding their promotion. The fourth category, Zone IV, represents a strong collection of outcome parameters influenced by several causal factors. These elements collectively contribute to the development of photovoltaic green roofs and have a significant impact. Centrality is a metric that can assess the importance of various influencing elements. Within the context of centrality, it can be observed that a higher numerical value corresponds to a greater level of importance for the influencing element. Therefore, it is imperative to pay attention to the set of solid causal factors (I) and the set of crucial resultant factors (IV). Zones I and IV are arranged in descending order of centrality, namely, A3, B4, A1, A2, C1, B2, B3, and D3.

4.2. Analysis of ISM Results

The purpose of setting the threshold value λ is to remove the influence relationship between indicators with less influence and simplify the system structure. Its size directly affects the composition of the adjacency matrix and further affects the division of the reachability matrix and system structure. The sum of the elements in the adjacency matrix’s row and column is considered the node degree, and the node degree is ranked in descending order to obtain the attenuation three-dimensional surface plot and scatter plot of each factor under different threshold values of λ (Figure 3). The principle of determining the value of λ is that the node is moderate, and the distribution diagram of the node degree of the two adjacent threshold values tends to be stable for the first time. The 3D surface plot in Figure 3A shows that the surface first stabilizes at two different threshold values. The approximate value range of the threshold is determined to be 0.10–0.14. By plotting the scatter plot under different values, it can be seen that the two lines coincide at λ = 0.11 and λ = 0.12 and stabilize first. Therefore, the threshold is set to λ = 0.12.

Subsequently, the reachability matrix is derived according to Step 8, as shown in

Table 6. Reachability matrix.

	A1	A2	A3	B1	B2	B3	B4	B5	C1	C2	C3	D1	D2	D3	D4	E1	E2	E3	F1	F2
A1	1	0	0	0	1	1	0	0	1	0	0	0	0	1	0	0	0	0	0	1
A2	0	1	0	0	1	1	0	0	1	0	0	1	0	1	0	0	0	1	0	0
A3	1	1	1	0	1	1	1	1	1	1	1	1	1	1	1	1	0	1	1	1
B1	0	0	0	1	0	0	0	0	0	0	0	0	1	1	1	0	0	0	0	0
B2	0	0	0	0	1	1	0	0	1	0	0	0	0	1	0	0	0	0	0	0
B3	0	0	0	0	0	1	0	0	1	0	0	0	0	1	0	0	0	0	0	0
B4	0	0	0	0	0	1	1	0	1	1	1	0	0	1	1	0	0	0	0	0
B5	0	0	0	0	0	1	1	1	1	1	1	0	1	1	1	0	0	0	0	0
C1	0	0	0	0	0	0	0	0	1	0	0	0	0	1	0	0	0	0	0	0
C2	0	0	0	0	0	1	0	0	1	1	0	0	0	1	0	0	0	0	0	0
C3	0	0	0	0	0	0	0	0	0	0	1	0	0	0	1	0	0	0	0	0
D1	0	0	0	0	0	0	0	0	0	0	0	1	0	1	0	0	0	0	0	0
D2	0	0	0	0	0	0	0	0	0	0	0	0	1	0	1	0	0	0	0	0
D3	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0	0
D4	0	0	0	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
E1	0	0	0	0	0	0	0	0	0	0	1	0	0	1	1	1	0	0	0	0
E2	0	1	0	0	1	1	0	0	1	0	0	1	0	1	0	0	1	1	0	0
E3	0	0	0	0	1	1	0	0	1	0	0	0	0	1	0	0	0	1	0	0
F1	0	0	0	0	1	1	0	0	1	0	0	0	0	1	0	0	0	0	1	0
F2	0	0	0	0	1	1	0	0	1	0	0	0	0	1	0	0	0	0	0	1

. The construction of the reachability set, the look-ahead set, and their intersection tables are determined based on the reachability matrix using Equations (12)–(14). The results are shown in

Table 7. Reachable set, look-ahead set, and their intersection.

Factors	Reachable Set (R)	Antecedent Set (Q)	Intersection (A = R∩Q)
A1	A1, B2, B3, C1, D3, F2	A1, A3	A1
A2	A2, B2, B3, C1, D1, D3, E3	A2, A3, E2	A2
A3	A1, A2, A3, B2, B3, B4, B5, C1, C2, C3, D1, D2, D3, D4, E1, E3, F1, F2	A3	A3
B1	B1, D2, D3, D4	B1	B1
B2	B2, B3, C1, D3	A1, A2, A3, B2, E2, E3, F1, F2	B2
B3	B3, C1, D3	A1, A2, A3, B2, B3, B4, B5, C2, E2, E3, F1, F2	B3
B4	B3, B4, C1, C2, C3, D3, D4	A3, B4, B5	B4
B5	B3, B4, B5, C1, C2, C3D2, D3, D4	A3, B5	B5
C1	C1, D3	A1, A2, A3, B2, B3, B4, B5, C1, C2, E2, E3, F1, F2	C1
C2	B3, C1, C2, D3	A3, B4, B5, C1	C2
C3	C3, D4	A3, B4, B5, C3, E1	C3
D1	D1, D3	A2, A3, D1, E2	D1
D2	D2, D4	A3, B1, B5, D2	D2
D3	D3	A1, A2, A3, B1, B2, B3, B4, B5, C1, C2, D1, D3, E1, E2, E2, F1, F2	D3
D4	D4	A3, B1, B4, B5, C3, D2, D4, E1	D4
E1	C3, D3, D4, E1	A3, E1	E1
E2	A2, B2, B3, C1, D1, D3, E2, E3	E2	E2
E3	B2, B3, C1, D3, E3	A2, A3, E2, E3	E3
F1	B2, B3, C1, D3, F1	A3, F1	F1
F2	B2, B3, C1, D3, F2	A1, A3, F2	F2

. In addition, Figure 4 shows the ISM illustrating the barriers to promoting photovoltaic green roofs in existing buildings.

The visual representation in Figure 4 illustrates the hierarchical structure model, which depicts the elements’ hierarchical arrangement and sequential progression. The hierarchical structure diagram illustrates the importance of various factors in the implementation and progression of photovoltaic green roofs in existing structures. These factors can be categorized into three levels: deep-rooted influencing factors, intermediate indirect influencing factors, and surface direct influencing factors. On the other hand, the causal relationship between various factors can be seen through the correlation in the hierarchical structure diagram; the mechanism and implementation path of promoting photovoltaic green roofs are obtained. The top-level elements in this model exert direct influencing effects, while the other factors contribute by acting on this level; the bottom-level elements are known as essential influencing elements and are crucial; the remaining levels act as intermediate transitional layers and intermediate influencing layers. Within the model, the top layer comprises actors with direct impact, which exert the most direct influence on the promotion of photovoltaic green roof retrofitting and are, in turn, affected by other factors. The bottom layer consists of fundamental impact factors that play a decisive role by influencing all intermediate and surface factors, thereby causing overall changes. The intermediate layers involve factors that play a transitional role and are influenced by the bottom layer and, in turn, influence surface factors. Figure 3 shows the seven levels of the structure. Layers 1 and 2 are the direct factors of the surface layer, including D3, D4, C3, C1, D1, and D2; Layers 3, 4, and 5 are the intermediate indirect factors, including B1, B2, B3, B4, C2, E1, E3, F1, and F2; Layers 6 and 7 are the deep-rooted influencing factors, including A1, A2, A3, B5, and E2. When improving the influencing factors, it should be improved from the basic factors to the direct factors, and changing the intermediate factors is more conducive to the positive cycle of promoting photovoltaic roofs in existing buildings. According to the ISM, macroeconomic policy dimension factors belong to deep-rooted influencing factors; project dimension and capital cost dimension factors belong to superficial direct influencing factors; and participant dimension factors, market dimension factors, and social dimension factors belong to intermediate indirect influencing factors. There are also some exceptions. For example, the uncertainty of investment return (C2) in the capital cost dimension is an intermediate indirect influencing factor; the lack of relevant talents (B5) in the participant dimension, and the cooperation mode (E2) in the market dimension belong to the deep-rooted influencing factors. The characteristics of the factors themselves determine this. For example, the uncertainty of return on investment (C2) cannot directly affect the implementation of the project, so it is an indirect factor; by contrast, the lack of relevant talents (B5) can affect the development of the industry and the technical level of enterprises, so it is a profound factor; the choice of cooperation mode (E2) directly determines the risks to be borne by all parties involved. For example, in the BOT mode, enterprises bear more significant risks. Due to the large amount of investment and long cycle, as far as investors are concerned, the investment payback period is also long, and the investment risk is high, so it is a profound fundamental factor.

4.3. Micmac Result Analysis

Each factor’s driving force and dependency value were calculated using Equations (15) and (16) in Step 11, as shown in

Table 8. Driving force and dependency values of each influencing factor.

Factors	Dependence	Driving Force	Factors	Dependence	Driving Force
A1	2	6	C3	5	2
A2	3	7	D1	4	2
A3	1	18	D2	4	2
B1	1	4	D3	17	1
B2	8	4	D4	8	1
B3	12	3	E1	2	4
B4	3	7	E2	1	8
B5	2	9	E3	4	5
C1	13	2	F1	2	5
C2	4	4	F2	3	5

. Each factor’s driving force and dependency value were used as coordinates, and the MICMAC analysis quadrant diagram was drawn; then, the average driving force and dependency value were used to determine the dividing line, which divided the diagram into four quadrants, as shown in Figure 5. The first, second, third, and fourth quadrants are autonomous clusters, dependent clusters, associated clusters, and independent clusters, respectively. The greater the dependency is, the more this component depends on other factors to be resolved, and the stronger the driving force is, the more this element can contribute to the resolution of other factors. Spontaneous factors include B1, C2, D1, D2, and E1. These factors have low driving power and dependency, but they play a connecting role and are the focus of promotion. Dependent factors include B2, B3, C1, C3, D3, and D4. The driving force of these factors is low, and the degree of dependence is high. Many other elements usually influence them. They are the direct factors associated with promotion obstacles and are vulnerable to other factors. The third quadrant has no influencing factor, indicating that the result is stable. The independent elements include nine items, namely, A1, A2, A3, B4, B5, E2, E3, F1 and F2. These factors, which are the core cause of promotion barriers and have a stronger influence on other factors but are less influenced by other factors, have a high driving force and low reliability. This component can be considered individually in the promotion of photovoltaic green roofs.

4.4. ANP Result Analysis

Using the reachability matrix, according to the results of the interaction between the indicators, a network model of barriers to the promotion of photovoltaic green roofs of existing buildings was built by using the appropriate software, as shown in Figure 6. The blue arrow in the figure indicates the existence of mutual influence factors between different dimensions; the black arrow shows that the indicator at the end of the arrow is influenced by the indicator at the beginning of the arrow between different dimensions. In contrast, the circular arrow indicates that there is a mutual influence relationship within the dimension group. The network structure diagram in Figure 6 indicates the interrelationships and mutual reinforcement between market dimension factors and macroeconomic policy dimension factors, as well as between capital cost dimension factors and participant dimension factors. Additionally, reciprocal relationships exist within the five dimensions of market factors, namely, project factors, capital cost factors, participant factors, and macroeconomic policy factors.

The evaluation matrix was evaluated by five experts using the 1–9 scale technique, and the weight of each element was determined using the super decision program. The matrix consistency test was successful for each calculation result. The unweighted and weighted supermatrices were established according to Steps 13 and 14. Step 15 involves the ANP weighting results, which are shown in Figure 7.

The mixed weight of each element was obtained in Step 16, and the final weight of each factor was obtained through normalization, as shown in

Table 9. Final weights.

Factors	Weight	Sort	Factors	Weight	Sort
A1	0.041	9	C3	0.019	17
A2	0.051	6	D1	0.038	11
A3	0.030	14	D2	0.059	5
B1	0.031	13	D3	0.237	1
B2	0.045	8	D4	0.079	3
B3	0.060	4	E1	0.033	12
B4	0.038	10	E2	0.046	7
B5	0.026	15	E3	0.014	20
C1	0.099	2	F1	0.018	18
C2	0.019	16	F2	0.017	19

. The ISM was combined with the final weight to draw a hierarchical structure model with a specified weight and the critical path was determined.

5. Discussion

Based on the analysis of the results in Section 4, combined with the analysis of DEMATEL-ISM-ANP, we identified the lack of incentive policies (A1), inadequate technical specifications, evaluation standards and systems (A2), the level of local economic development (A3), the level of awareness of the population (B2), the willingness of the population (B3), the technological problems of enterprises (B4), the lack of relevant talents (B5), the lack of capital investment (C1), and the mode of cooperation (E2) as crucial factors.

The lack of incentive policies (A1); the soundness of technical specifications, evaluation standards, and systems (A2); and the level of local economic development (A3) are macroeconomic policy dimension factors, which are strong causal factors. They are also the deep-rooted influencing factors that restrict the promotion of green roofs and significantly impact other factors. The level of economic development is one of the critical factors determining the photovoltaic green roof-related technology and demand, and a higher level of economic development can provide financial support for photovoltaic green roof retrofitting technology for existing buildings and develop related technical specifications and incentive policies, which in turn bring more market opportunities. In order to realize sustainable urban development, build sponge cities, and achieve the “dual-carbon goal”, photovoltaic green roof retrofitting for existing buildings is a promising development direction, and the level of economic development determines the support for its advancement. However, the low weight of the local economic development level suggests that this factor is more difficult to change.

In contrast, the lack of incentive policies and the imperfection of technical specifications and evaluation standard systems have higher weights, ranking sixth and ninth, which can be improved by making efforts to overcome these challenges. The lack of technical specifications and evaluation standard system will lead to the lack of technical knowledge and experience of enterprises, and it is not known whether the construction standards and acceptance meet the requirements when the building roof is retrofitted. In China, there are many policies to promote photovoltaic roofing. However, there is no specific policy for photovoltaic green roofs, and many researchers have shown that incentive policies play a crucial role in promoting technology [16,17,18,19], which is also applicable to photovoltaic green roofs. On the one hand, incentive policies can motivate enterprises to provide materials for photovoltaic green roofs. On the other hand, subsidies and consumer preferences will increase the willingness to pay, promoting the high-quality development of photovoltaic green roofs.

The four factors of residents’ awareness (B2), residents’ willingness (B3), enterprises’ technical problems (B4), and lack of related talents (B5) belong to the dimensions of participating subjects. The lack of talent will lead to the need for more relevant technology, increasing the difficulty of retrofitting. Therefore, the government should provide professional education and training on photovoltaic green roof retrofitting to ensure the development of related professionals. Residents’ level of awareness and willingness will result from the combined effect of other factors. Demographic characteristics (F1) will affect the residents’ awareness, and well-educated and young people tend to be more receptive to new technologies; the level of local economic development (A3) implies the level of residents’ income, which determines the residents’ willingness to spend money, and the level of residents’ awareness also affects the residents’ willingness to invest. Therefore, photovoltaic green roofs can be positively promoted by improving residents’ awareness and willingness to invest. Enterprise technology means whether it can contract projects and is robust; often in a project, enterprises are more willing to promote photovoltaic green roofs to obtain more profits. In order to improve the competitiveness of enterprise technology, on the one hand, it is necessary to absorb relevant technical talents, and on the other hand, the research and development of technology should be increased.

The lack of capital investment (C1) is an important result factor and ranks second in weight, which is a direct factor affecting the promotion of the area. In promoting photovoltaic green roofs, it is necessary to focus on introducing multiple financing channels, including government and social capital investment.

The cooperation mode (E2) belongs to the deep-level influencing factors and ranks high in weight but can also establish multiple cooperation modes in promoting photovoltaic green roof renovation. The government, social capital, and neighborhood owners are the main participants of the retrofit, and different cooperation modes can be developed according to the actual conditions of a project, such as the social capital, the interest of the owner, and the interest of the neighborhood.

6. Conclusions and Prospects

Retrofitting existing buildings with photovoltaic green roofs is essential for promoting urban renewal and building an environmentally sustainable city. This study examines the correlation between influential factors that affect the promotion of PV green roof retrofitting in existing buildings using a fuzzy DEMATEL-ISM-ANP research methodology. The DEMATEL method was used to perform matrix operations on the influencing factors and obtain each influencing factor’s order of centrality and causality. The ISM method was then used to create a hierarchical map of the influencing factors and determine the direction between them. The analysis of the DEMATEL-ISM shows that the fundamental factors studied in the ISM are similar to the highest-ranked factors in the DEMATEL model regarding causality. In addition, the outcome factors obtained from the DEMATEL model are consistent with the direct influencing factors identified through the ISM analysis. This also highlights the congruence in the importance and type classification of influencing factors evident in both methods, reinforcing the scientific validity and accuracy of the model analysis. The MICMAC technique was then used to differentiate the quadrants based on their dependency and driver object quadrants, allowing for a comprehensive evaluation of quadrant attributes and factor conditions. It was confirmed that the independent factors were consistent with the primary cause factors in the DEMATEL and the underlying factors in the ISM. The final weights of the factors were then determined by integrating the DEMATEL and ANP methods, allowing for the development of more effective improvement strategies. The results of this study provide practical guidance for promoting the use of PV green roofs in existing buildings. The conclusions of this paper are as follows:

• Through the investigation of constraints on the promotion of photovoltaic green roof renovation for existing buildings, the effectiveness of the fuzzy DEMATEL-ISM-ANP method in studying coupling relationships, the degree of influence factors, and the method of determining weights were verified.
• A literature review and expert suggestions were considered to summarize the factors influencing the promotion of PV green roof retrofits for existing buildings. Twenty indicators were finally identified and categorized into six groups: macroeconomic policy, participant organization, capital cost, project, market, and social factors.
• In determining the adjacency matrix of the ISM, the node degree method was introduced to determine the threshold value, which is more objective than the previously used expert determination method.
• Lack of incentive policies (A1), imperfect technical specifications and evaluation standard systems (A2), local economic development level (A3), enterprise technical problems (B4), lack of relevant talents (B5), and cooperation mode (E2) are key factors with strong driving force and low dependency, which influence other factors and affect the overall promotion. However, the dependent factors, namely, residents’ awareness (B2) and willingness (B3), are also key factors that need attention due to their strong influence on the results and high weights. Adjustments are needed not only in macroeconomic policies but also in stakeholder involvement to promote photovoltaic green roofs.
• Direct influencing factors, namely, C1, C3, D1, D2, D3, and D4, are most prominent in the system. They are mainly related to costs and project-specific factors. The weight of direct influencing factors is generally higher. However, due to the difficulty of changing them, improvements from fundamental to direct factors are necessary to achieve a positive cycle.

Since this study mainly examines the interaction of factors affecting the promotion of photovoltaic green roofs in existing buildings in China, the results can be applied to countries and regions with similar development as China. However, this study has some limitations. Although the data from experts are authoritative and representative, the preference of experts will inevitably lead to a certain degree of subjectivity. In future work, it is also necessary to further evaluate the importance of critical barriers and formulate more reasonable suggestions and strategies for the development of photovoltaic green roofs.