## 4 Case Study
### Carbon Footprint Influence Factor Analysis Based on DEMATEL-ISM-MICMAC
#### 4.3.1 Analysis of DEMATEL Results  
Applying Equations (9) and (10) to the direct impact matrix derived from the experts' scores yields an integrated impact matrix \(T\), as shown in Table 5.  
The integrated impact matrix \(T\) was processed using MATLAB R2022b software to determine the degree of influence, degree of being affected, causality, and centrality. The centrality was then ranked. As shown in Table 6.  
The centrality-causality diagram is depicted according to Table 6 (Figure 5).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Factors** & **Degree of Influence** & **Degree of Being Affected** & **Causality** & **Centrality** & **Centrality Ranking** \\ \hline S\({}_{1}\) & 0.361 & 1.261 & \(-\)0.900 & 1.622 & 10 \\ S\({}_{2}\) & 0.319 & 1.555 & \(-\)1.235 & 1.874 & 5 \\ S\({}_{3}\) & 0.894 & 0.154 & 0.740 & 1.048 & 16 \\ S\({}_{4}\) & 1.675 & 0.264 & 1.412 & 1.939 & 4 \\ S\({}_{5}\) & 0.949 & 1.158 & \(-\)0.209 & 2.107 & 3 \\ S\({}_{6}\) & 0.277 & 1.588 & \(-\)1.311 & 1.866 & 6 \\ S\({}_{7}\) & 1.085 & 1.130 & \(-\)0.045 & 2.215 & 1 \\ S\({}_{8}\) & 1.198 & 0.585 & 0.612 & 1.783 & 7 \\ S\({}_{9}\) & 0.430 & 0.797 & \(-\)0.367 & 1.227 & 14 \\ S\({}_{10}\) & 0.512 & 0.664 & \(-\)0.152 & 1.176 & 15 \\ S\({}_{11}\) & 0.922 & 1.202 & \(-\)0.280 & 2.123 & 2 \\ S\({}_{12}\) & 0.238 & 0.551 & \(-\)0.313 & 0.789 & 17 \\ S\({}_{13}\) & 0.252 & 1.136 & \(-\)0.884 & 1.388 & 13 \\ S\({}_{14}\) & 0.574 & 0.000 & 0.574 & 0.574 & 18 \\ S\({}_{15}\) & 1.657 & 0.000 & 1.657 & 1.657 & 9 \\ S\({}_{16}\) & 0.641 & 1.110 & \(-\)0.468 & 1.751 & 8 \\ S\({}_{17}\) & 0.996 & 0.391 & 0.605 & 1.388 & 12 \\ S\({}_{18}\) & 1.048 & 0.485 & 0.563 & 1.534 & 11 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Calculation results of influence, cause and centrality of impact factors, and centrality ranking.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c} \hline \hline
**Factors** & **S\({}_{1}\)** & **S\({}_{2}\)** & **S\({}_{3}\)** & **S\({}_{4}\)** & **S\({}_{5}\)** & **S\({}_{6}\)** & **S\({}_{7}\)** & **S\({}_{8}\)** & **S\({}_{9}\)** & **S\({}_{10}\)** & **S\({}_{11}\)** & **S\({}_{12}\)** & **S\({}_{13}\)** & **S\({}_{14}\)** & **S\({}_{15}\)** & **S\({}_{16}\)** & **S\({}_{17}\)** & **S\({}_{18}\)** \\ \hline S\({1. Regarding the extent of impact, the top three factors are raw material energy consumption (S4), construction planning and organization (S15), transportation energy type (S6), and waste disposal (S2). This indicates that these three factors have the greatest importance in influencing the other factors.
2. In terms of centrality, the three factors of transportation distance (S7), packaging and containers (S11), and transportation tool selection (S5) have larger values of centrality. Therefore, the carbon footprint in the materialization stage of prefabricated housing should focus on the management of building material transportation.
3. The causal factors are, in descending order, construction planning and organization (S15), raw material energy consumption (S4), packaging and containers (S11), component production process (S8), construction assembly (S17), transportation emission factors (S14), and losses during construction (S18). These factors are the causal factors in the carbon footprint of the materialization phase of the assembled house, and should be given high priority. Among them, packaging and containers (S11) belong to the prefabricated component processing stage, demonstrating that the carbon footprint of the materialization stage of constructed dwellings depends on packaging and containers.
4. The top three resultant factors are material selection and production (S1), waste disposal (S2), and type of energy transportation (S6), suggesting that at the materialization stage of completed houses, these three parameters are more likely to be modified by other aspects in the carbon footprint process.