## 4 Results and Discussion  
The methodology based on IT2 FLS was implemented on MATLAB (MATLAB is a registered trademark of The MathWorks, Inc.) using the provided Fuzzy Logic Toolbox. The version of the IT2 FLS toolbox used allows the intuitive implementation of IT2 FLSs, where it can cover all the phases of its design. Furthermore, the proposed method has been examined by evaluating the buildings database of the Bingol earthquake (2003) and Duzce earthquake (1999) in Turkey. For this purpose, the information of 28 reinforced concrete buildings in Bingol, and 484 reinforced concrete buildings in Duzce have been selected from the SERU (Structural Engineering Research Unit) database [49], which was collected from the street survey by a team of researchers from Middle East Technical University (METU), Ankara. The Bingol earthquake struck with a magnitude \(M_{w}=6.4\), reported peak ground acceleration (PGA) 0.556 g and PGV 34.5 cm/s [50]. Moreover, studies by [PERSON] et al. [51] and [PERSON] et al. [12] provide detailed technical information about the characteristics of the Bingol earthquake and the information about the observed buildings, respectively. A report from the observed damage to the buildings in different places in Bingol stated that damages were mostly due to the properties of structures, and not due to the foundation conditions or any ground deformation [52]. Therefore, it has been assumed that for assessing the vulnerability of the buildings in Bingol there are no corrections or additional parameters required for different soil conditions, and the soil condition of the selected area are quite uniform, predominantly granular alluvial deposits, which are dense to very dense (Soil Type A or B) [53]. In 12 November 1999, a powerful earthquake struck the city of Duzce (Turkey) within a magnitude of \(M_{w}=7.1\), PGA 0.821 g and PGV 66.9 m/s [53]. A district in Duzce with a total number of 484 three- to six-story RC buildings was surveyed and collected by SERU [49] after the Duzce earthquake. Moreover, soil conditions were uniform, and stiff clays with interbedded layers of dense sands and gravels. The measured (\(V_{s}\) 30) at DZC station was 294 m/s, \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Rule No.**} & \multicolumn{8}{c}{**Input Variable**} & \multicolumn{8}{c}{**Output**} \\ \cline{2-13}  & **NS** & **PI** & **VI** & **Age** & **ST** & **PCV** & **(Damage)** \\ \hline
1 & Low & and & No & and & No & and & Old & and & A/B & and & Low & Then & No damage \\ \hline... &... &... &... &... &... &... &... &... &... &... &... &... &... \\ \hline
171 & Medium & and & Yes & and & No & and & Old & and & E & and & Medium & Then & Severe \\ \hline... &... &... &... &... &... &... &... &... &... &... &... &... &... \\ \hline
324 & High & and & Yes & and & Yes & and & New & and & E & and & High & Then & Severe \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The structure of the T2 FLS in this study. Figure 3: Generalized bell-shaped membership functions for damage as output variable. which categorized the soil as a ground type C according to classification in this study, and topography was flat over the surveyed district [54]. Duzce is located under a high seismic zone and the information extracted from the database was similar to Bingol. Figures 4 and 5 show the distribution of the observed damage categories of buildings in Bingol and Duzce, respectively [49]. Moreover, the estimation based on the fuzzy synthetic evaluation proposed by [PERSON] [55] on the same Bingol dataset, and the estimation by the proposed method in this paper based on IT2 FLS can be seen. It shows that the proposed method has a good agreement with the observed damage state distributions. From the data in Figures 4 and 5, it can be manifested that the proposed method considered safety factor by overestimating the damage states more than moderate and underestimate low damage and no damage because of caring more about safety and expecting higher risk.