# Development of Fire Safety Assessment Model for Buildings Using Analytic Hierarchy Process
## 5 Model Development
### Pairwise Comparison Matrices  
Pairwise comparison is applied to determine the AHP weights of the main factors and sub-factors for the fire hazard and fire safety hierarchies. Both hierarchies consist of two levels, as previously displayed in Figures 6 and 7. Within the hazard hierarchy, the building hazard index is evaluated by measuring its compliance against four main factors: user behavior, access requirements, building requirements, and emergency design. Tables 6 and 7 show the calculation of the AHP weights of the main factors and sub-factors using the pairwise comparison method. +++ \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Level 1**} & **User** & **Access** & **Building** & **Design for** & **\(n\)th Root of** & **Eigenvector** \\  & **Behavior** & **Requirements** & **Requirements** & **Emergency** & **(ABCD)** & **(Relative** \\  & & & & & & **Product Values** & **Weight**) \\ \hline User behavior & 1.00 & 0.20 & 0.20 & 0.20 & 0.299 & 0.059 \\ Access requirements & 5.00 & 1.00 & 0.33 & 0.33 & 0.863 & 0.169 \\ Building requirements & 5.00 & 3.00 & 1.00 & 1.00 & 1.968 & 0.386 \\ Design for emergency & 5.00 & 3.00 & 1.00 & 1.00 & 1.968 & 0.386 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Pairwise comparison for hazard factors level 1. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**User Behavior**} & **Building Usage** & **Dangerous** & **Occupant** & **\(n\)th Root of** & **Eigenvector** \\  & **Activities** & **Awareness** & **Product Values** & **(Relative** \\  & & & & & **Product Values** & **Weight**) \\ \hline Building usage & 1 & 1/3 & 5 & 1.186 & 0.297 \\ Dangerous activities & 3 & 1 & 5 & 2.466 & 0.618 \\ Occupant awareness & 1/5 & 1/5 & 1 & 0.342 & 0.086 \\ \hline \multirow{2}{*}{**Access Requirements**} & \multirow{2}{*}{**Access Roads**} & \multirow{2}{*}{**Distance to the Entrance**} & **\(n\)th Root of** & **Eigenvector** \\  & & & & **(ABCD)** & **(Relative** \\  & & & & **Product Values** & **Weight**) \\ \hline Access roads & 1 & 1 & 1.000 & 0.500 \\ Distance to the entrance & 1 & 1 & 1.000 & 0.500 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Pairwise comparison for hazard factors level 2. Figure 7: Fire safety assessment model. In this study, five main fire safety attributes for buildings are defined--namely, fire prevention, fire detection, fire containment, firefighting, and fire management. Within the safety hierarchy, Tables 8 and 9 show the calculation of the AHP weights of the main factors and sub-factors using the pairwise comparison method. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Building** & **Building Type** & **Material** & **Electrical** & **Building** & **\(n\)th Root of** & **Eigenvector** \\
**Requirements** & **and Use** & **Requirements** & **Connections** & **Content** & **(ABCD)** & **(Relative** \\  & & & & & & **Product Values** & **Weight**) \\ \hline Building type and use & 1 & 1/3 & 1/5 & 1 & 0.508 & 0.094 \\ Material requirements & 3 & 1 & 1/3 & 5 & 1.495 & 0.277 \\ Electrical connections & 5 & 3 & 1 & 5 & 2.943 & 0.546 \\ Building contents & 1 & 1/5 & 1/5 & 1 & 0.447 & 0.083 \\ \hline
**Design for** & & & & & **\(n\)th Root of** & **Eigenvector** \\
**Emergency** & **Fire Containment** & **Emergency Exit** & **Assembly Points** & **Assembly Points** & **(ABCD)** & **(Relative** \\  & & & & & **Product Values** & **Weight**) \\ \hline Fire containment & 1 & 1/3 & 3 & 1.000 & 0.287 \\ Emergency exit & 3 & 1 & 3 & 2.080 & 0.597 \\ Assembly points & 1/3 & 1/5 & 1 & 0.405 & 0.116 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._