# Integral Seismic Risk Assessment through Fuzzy Models
## 5 Results and Discussion
### Results for Bogota  
Although Colombia's capital is divided into 20 administrative localities, in this study, we used only 19, since the 20 th corresponds mainly to the rural area of the city. As before, to estimate social aggravation for each district, we used statistical and demographic data as reported in [24]. The left-hand-side plots of Figure 8 show aggravation levels obtained by means of the proposed fuzzy model (upper plot) and [PERSON]'s equation (lower plot). In this case, the general aggravation level seems to be underestimated by the fuzzy model when compared with [PERSON]'s equation, or index method. However, both models estimated that the highest values of aggravation are at the southwest part of the city, corresponding to Districts (4)-(8). The east part of the city remains with medium-low, while the northwest part of the city presents medium-high aggravation values. The index method reaches a very-high value at the southwest part of the city while the northern part presents mostly a medium-low aggravation value. Figure 9 shows the numerical values of the aggravation levels for the 19 administrative districts of Bogota, obtained through the two methods. As in the Barcelona case, the trend is similar to that obtained by the index method, although there is a difference in the numerical values. Physical risk levels were estimated using a probabilistic damage seismic scenario as a base, which considered an earthquake of close to 0.2g of rock acceleration, and which was studied by the Universidad de Los Andes in 1997 [34; 35]. The center plots of Figure 8 show the physical risk spatial patterns of fuzzy and index methods, respectively. Both estimate the highest physical risk values in the northern part of the city (Districts: (1), (2), (11), (12), (13), and (17)). Figure 10 shows the physical risk numeric values over the 19 administrative districts of Bogota estimated by both methods. It is clear that [PERSON]'s equation, or index method, present the lowest values for almost all city localities, while the fuzzy model estimates are as much as twice as high for the same locations. Figure 7: Total Risk values for the 248 Barcelona small statistical areas (ZEP). Figure 8: Risk components obtained for Bogota city by: the fuzzy model (upper part) and the index model (lower part). From left to right: social aggravation, physical risk, and total seismic risk. Significant values of each component have been highlighted to show a measure of how the assumption of compensability can lead towards different risk spatial patterns. Figure 9: Aggravation values obtained for the 19 administrative localities of Bogota with the index method and the proposed fuzzy model. The right-hand-side plots of Figure 8 show the estimated spatial patterns of total risk, according to the fuzzy model (upper plot) and the index method (lower plot), respectively. The fuzzy model estimates that the highest levels of risk are present mostly in the south and the center parts of the city. In contrast, the index method determines the highest risk levels for the northern part of the city and only a small region in the south. Figure 11 shows the total risk numerical values over the 19 districts of Bogota. The variability estimated by the fuzzy model is similar to that estimated by the index method, especially at the right-hand side of the plot. Figure 11: Total Risk values obtained for the 19 administrative localities of Bogota with the index method and the proposed fuzzy model. Figure 10: Physical Risk values obtained for the 19 administrative localities of Bogota with the index method and the proposed fuzzy model. Comparison of Seismic Risk Spatial Distribution's Patterns of the Fuzzy Model and the Index Method in Barcelona and Bogota  
It is worth analyzing the differences carefully among total risk spatial patterns of both methodologies where the advantages in performing a non-linear aggregation of indicators through fuzzy methods can be seen.