## 4 Case Study
### Carbon Footprint Influence Factor Analysis Based on DEMATEL-ISM-MICMAC
#### 4.3.2 Analysis of ISM Results  
The contextual interactions among the identified carbon footprint-influencing variables may vary in degree. The contextual linkages between the carbon footprint-influencing elements yield SSIMs in accordance with step 4 of the ISM technique. Such links can be detected using ISM in order to derive a relationship model. According to expert comments and the impact of each piece on the other, contextual linkages are created.  
For example, factor S1 (\"material selection and production\"), is compared with factor S10 (\"production size and volume\") for their contextual relationship. S10 influences S1, hence the contextual relationship of 'A' is considered. In a similar vein, other contextual linkages can be inferred, and the ensuing matrix can be filled by comparing the carbon footprint influencers S1-S18. The links between the effects of carbon footprints are displayed in Table 7.  
Figure 5: Centrality–causality degree diagram.  
The reachable matrix \(F\) is formed using the binary numbers '1' and '0'. The different symbols used to represent contextual relationships ('V', 'A', 'X', and 'O') can be replaced by '1' and '0' in accordance with the previously established principles, as outlined in step 5. The reachability matrix \(F\) is shown in Table 8.  
The reachability series, the antecedent set, and the intersection set are determined from the reachability matrix \(F\), as shown in Table 9.  
To establish the carbon footprint influence factors of the stage of materialization of the prefabricated housing hierarchy framework, as depicted in Figure 6, the reachable matrix f processing is used to obtain the reachability set \(R(S_{i})\), the antecedent set \(A(S_{i})\), and the intersection set. Then, Formula (11) is applied based on the outcomes of the hierarchy's priority division to collect five layers.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c  
1. L6 belongs to the deep-level factor, which should pay great attention to construction planning and organization (S\({}_{15}\)).
2. L1 belongs to the shallow sub-factors, and the issues at this level primarily pertain to the delivery of prefabricated components and the production and processing of construction materials, indicating that these two phases will directly affect the manufactured home's carbon footprint.
3. L2 to L4 belong to the middle-level factors, and they will have an impact on the shallower-level factors. Among them, transportation tool selection (S\({}_{5}\)) and transportation distance (S\({}_{7}\)) have a strong correlation. Therefore, in the greenhouse gas emissions investigation of the materialization stage of prefabricated housing, it is imperative to enhance the handling of building material transportation in order to reduce the carbon emissions of the building process.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factors** & **Reachability Set** & **Antecedent Set** & **Intersection Set** \\ \hline S\({}_{1}\) & 1 & 1,3,4,5,7,8,10,11,15,18 & 1 \\ S\({}_{2}\) & 2 & 2,3,4,5,7,8,11,15,18 & 2 \\ S\({}_{3}\) & 1,2,3,5,6,11 & 3 & 3