## 3 Research Methodology
### Application of MCDM Methods  
Various seismic parameters used to perform the MCDM methods have been enlisted and explained such as: Seismic zone (SZ), Type of building (B), Vertical irregularity (VI), Plan irregularity (PI), Pre-code, Post benchmark and code detailing (C), Soil type (ST), Number of stories (N), Apparent building quality (Q). The decision matrix performed for all methods above remains the same, which was scaled from 1 to 9 using general scale. It classifies as the scale 1 indicates no influence and scale 9 indicates severe or a high influence. Decision matrix has formed based on ranking given for all structures according to the parameters. The size of the decision matrix can be \(28\times 8\), as the data have 28 buildings and 8 parameters. To create a decision matrix based on the general scale, following rankings were used for each parameter. * Seismic zone: The seismic zone has been considered as per FEMA P-154, it classifies the seismic zone ranks from 1 to 9 shown in Table 4. All structures in the data has the 'High' seismic zone, for that ranking 7 has been assigned. * Building type: The dataset has two types of structures, which are classified as C2 and C3 according to the vulnerability scale from EMS 98 [46]. * Vertical irregularities: Vertical irregularities considered in RVS methods the same conditions are taken here. The ranks for vertical irregularities are tabulated in Table 5.
* Plan irregularities: The same conditions are taken here for plan irregularities considered in RVS. The ranks for horizontal irregularities are tabulated in Table 6.
* Code parameter: For the parameter 'year of construction' there are only 3 rankings as provided in Table 7.
* Soil type: As per FEMA P-154 soil has classified in 5 types and different ranks have given to each soil type in Table 8. From the data all buildings are located over the very dense soil, and number 5 has been given for that rank. * Number of stories: Depending on the number of stories for each structure, the ranking has provided in Table 9.
* Building quality: The quality of building has been classified in 3 categories such as good, moderate, and poor, which their respective rankings are given in Table 10. \begin{table}
\begin{tabular}{c c} \hline \hline
**Seismic Zone** & **Ranking** \\ \hline Low & 1 \\ \hline Moderate & 3 \\ \hline Moderate high & 5 \\ \hline High & 7 \\ \hline Very high & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: ‘Seismic zone’ rankings considered in Multi-Criteria Decision Making (MCDM) methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**No. of Vertical Irregularities** & **Ranking** \\ \hline
0 & 1 \\ \hline
1 & 2 \\ \hline
2 & 3 \\ \hline
3 & 4 \\ \hline
4 & 5 \\ \hline
5 & 6 \\ \hline
6,7 & 7 \\ \hline
8 & 8 \\ \hline
9 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: ‘Vertical irregularity’ rankings considered in MCDM methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**No. of Plan Irregularities** & **Ranking** \\ \hline
0 & 1 \\ \hline
1 & 2 \\ \hline
2 & 3 \\ \hline
3 & 5 \\ \hline
4 & 7 \\ \hline
5 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: ’Plan irregularity’ rankings considered in MCDM methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**Soil Type** & **Ranking** \\ \hline Hard rock & 1 \\ \hline Rock & 3 \\ \hline Very dense soil—soft rock & 5 \\ \hline Stiff soil & 7 \\ \hline Soft clay & 8 \\ \hline Poor soil & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: ’Soil type’ rankings considered in MCDM methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**No. of Plan Irregularities** & **Ranking** \\ \hline
0 & 1 \\ \hline
1 & 2 \\ \hline
2 & 3 \\ \hline
3 & 5 \\ \hline
4 & 7 \\ \hline
5 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: ’Code parameter’ rankings considered in MCDM methods. \begin{table}
\begin{tabular}{c c} \hline \hline
**Quality** & **Ranking** \\ \hline Good & 2 \\ \hline Moderate & 4 \\ \hline Poor & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: ’Building quality’ rankings considered in MCDM methods.