## 5 Conclusions  
To summarize, it can be observed that the selected MCDM methods are reliable for RVS. In this study, the data of 28 reinforced concrete buildings have been collected from the walk-down survey conducted by the METU team in Bingol, Turkey, after the Bingol earthquake in 2003. Furthermore, MCDM methods have been implemented to determine the damage grades for the given post-earthquake building data. Firstly, the validation of the damage index from the MCDM methods and the actual damage state of structures during the Bingol earthquake have been accomplished. After that, the comparison of the actual damage state, and damage index from the MCDM methods based on three different RVS methods have been executed. From the analogical study, it can be concluded that the MCDM method TOPSIS-W1 contributes more relevant results than rest MCDM methods performed in RVS of structures. The MCDM methods performed in this research have been enlisted in Table 17 with descending order based on the obtained results. In the discussion of executed MCDM methods, TOPSIS-W1 has achieved the top rank. On the second rank, RAHP has been observed but only in case of safety factor because where the similarities were considered, RAHP had the least rank. The outputs of TOPSIS-W2 and W3 were closer when compared to the actual damage than the output of WSM-W2 and W-3, which can be observed from the similarity plot. So, WSM-W2 and W3 were ranked after TOPSIS-W2 and W3. Further, AHP 1, AHP 2, WPM-W2, and W-3 have provided similar plots, so they are one the same rank and listed after methods WSM-W2 and -W3. The reason for their lower ranks is that they had analyzed a smaller number of buildings in damage state 1 compared to WSM-W2, and W-3 methods. In the end, WSM-W1 stands on the last rank due to the lower building application in damage state 1. Also observed in similarities \begin{table}
\begin{tabular}{c c} \hline \hline
**MCDM Method** & **Ranking** \\ \hline TOPSIS-W1 & 1 \\ \hline RAHP & 2 \\ \hline TOPSIS-W2 \& W3 & 3 \\ \hline WSM-W2 \& W3 & 4 \\ \hline AHP 1 \& 2, WPM-W2 \& W3 & 5 \\ \hline WSM-W1 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Ranking of MCDM methods used based on results. Figure 11: Percentage of each damage group assessed by different MCDM methods and actual damage. 2 and 3, the results are pretty close to the actual damage state of the structures. The ranking of the methods could not affect the variation in the distribution of parameters. It can be noticed that the results may differ with the larger amount of data set. Therefore, for future works, the results can be improved according to the varied rate of buildings through performing MCDM methods. For future actions, the complex MCDM methods such as PROMOTHEE, ELECTRE, and many hybrid methods can help identify a more accurate way for this research problem. Moreover, the MCDM methods' reliability can be checked with other vulnerability cases, which may involve the damage assessment of structures and seismic prioritization based on the seismic vulnerability of the affected regions. Conceptualization, E.H. and T.L. ; methodology, E.H. and K.M. ; validation, T.L. and E.H.; formal analysis, E.H. and K.M. ; investigation, K.J. and K.M. ; resources, E.H.; data curation, K.M. and K.J. ; writing--original draft preparation, E.H., K.J., K.M. and S.E.A.H. ; writing--review and editing, E.H., K.J. and S.E.A.H. ; visualization, E.H. and K.J. ; supervision, E.H., T.L. ; project administration, E.H. and T.L. All authors have read and agreed to the published version of the manuscript. This research received no external funding. We acknowledge the support of the German Research Foundation (DFG) and the Bauhaus-Universitat Weimar within the Open-Access Publishing Programme. The authors declare no conflict of interest.