## 4 Results and Discussions
### Analogy Using Similarities  
Here is the comparison between damage states of RVS methods to the MCDM methods. Figure 3 represents all 5 similarities used for MCDM methods.  
The plot in Figure 3 shows that TOPSIS-W2, W3, WSM-W2, W-3, and WPM-W2, W-3 have contributed to almost exact results. That means normalization of values in the weight calculation process has been done either taking the sum of all numbers or through considering the number. It could not affect TOPSIS, WSM, and WPM, but it has influenced RAHP. Figure 3 shows, for similarity 1, WSM-W2, W3, and WPM-W2, W-3 have provided better results as they have captured almost 36 percent of buildings similar to exact damage, which is followed by TOPSIS with around 33 percent. The rest of the methods gave less than 20 percent of buildings. Theoretically, expectations from RAHP were higher to provide good results compared to AHP 1 and 2, but in this case, the results were opposite. TOPSIS-W1 performed better than TOPSIS-W2, W3, plus it has the best result compared to the rest of the methods for the case of similarities 2, 3, 4, and 5 which is followed by TOPSIS-W2, W3. Moreover, AHP 2 has provided good results after TOPSIS, while in similarities 2 and 3 AHP 2 and TOPSIS-W2, W3 gave the same results.  
Consequently, the bar chat shows that the TOPSIS-W1 method was better than other methods except in similarity 1; otherwise, WSM-W2, W3, and WPM-W2, W3 could be better. AHP 2 and TOPSIS-W2, W3 were also better methods after the previous ones for similarities 2 and 3. Hence, TOPSIS-W1, W2, AHP 2, and WSM-W2 have been compared further with RVS methodologies. The following Figure 4 shows the comparison of results from the real damage state and proposed RVS based on MCDM methods.  
Among MCDM methods, WSM-W2, W3, and WPM-W2, W3 have contributed better results. In the case of other similarities, TOPSIS-W1 gave better results than other MCDM methods. Furthermore, in Figure 5, the comparison of all MCDM methods with the actual damage has been shown. Figure 5 indicated that, for the MCDM methods, TOPSIS-W1 and RAHP have an estimated larger group of buildings which are closer to the actual damage, which includes damage grades 1 and 2 for the output. After that, the results of TOPSIS-W2, W3, and WSM-W2, W3 methods were close to the actual damage, but to compare it with the previous methods, the count was quite less. Amidst all the MCDM methods used in this research, TOPSIS-W1 has contributed to better results than RVS methods followed by WSM-W2, W3, and TOPSIS-W2, W3. In consideration of the WSM-W2, W3, and TOPSIS-W2, W3 performed as second better methods.  
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Parameters** **Considered in MCDM** & **Indian RVS Ranking** & **FEMA P-154 Ranking** & **Turkish RVS Ranking** & **Average Rank** & **Ranking on Rank** **[1 to 9 Scale]** \\ \hline Seismic zone & 1 & 1 & 1 & 1 & 9 \\ \hline Building type & 1 & 1 & & 1.5 & 8 \\ \hline Vertical Irregularity & 4 & 5 & 4.6 & 4.5 & 5 \\ \hline Plan Irregularity & 6 & 3.5 & & 5 & 4 \\ \hline Code/benchmark & 3 & 2 & & 3 & 6 \\ \hline Soil type & 5 & 3 & 1 & 3 & 6 \\ \hline No. of stories & 2 & 3 & 1 & 2 & 7 \\ \hline Building quality & & & 4 & 4.5 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Ranking of parameters based on the comparison of methods for ranks scaled from 1 to 9.  
Figure 4: Similarities illustrated by the percentage of buildings for all proposed MCDM methods.  
Figure 5: Percentage of buildings belongs to damage state 1 from MCDM methods.  
Figure 3: Similarities shown according to the selected MCDM methods by percentage of buildings.