## 3 Results
### Sensitivity Analysis on the Choice of Weights  
As introduced in Section 2, the sensitivity analysis on the weights was performed by first increasing the weight of each individual criterion at a time, and then assuming the simultaneous increase in the weights of the three \"exposure\"-related criteria, namely land use, population density, and strategic buildings. Specifically, the weights were changed according to Scenarios 0, 1, 2, and 3 described in Table 3.  
For the sake of brevity, we present hereafter the results obtained by assuming the usual preference function. For the reader's convenience, the results are reported as maps, as in the previous sections. In the first part of the analysis, the criteria are changed according to the following order: Flood hazard, PGA, land use, strategic buildings, age of buildings, and population density. Hereafter, we omit the maps obtained for the changes of the weights relating to the criteria of strategic buildings and age of buildings, for brevity. Figures 13 and 14 illustrate the various risk maps obtained by increasing the weights. \begin{table}
\begin{tabular}{c c c c c} \hline
**Rank** & **Alternatives** & \(\mathbf{\Theta}\) & \(\mathbf{\Theta^{+}}\) & \(\mathbf{\Theta^{-}}\) \\ \hline
1 & Cento & 0.4532 & 0.4849 & 0.0317 \\ \hline
2 & Ferrara & 0.3769 & 0.4123 & 0.0354 \\ \hline
3 & Tresigallo & 0.2051 & 0.2613 & 0.0562 \\ \hline
4 & Vigarano Mainarda & 0.1219 & 0.2185 & 0.0966 \\ \hline
5 & Mirabello+ Sant’Agostino & 0.078 & 0.1835 & 0.1056 \\ \hline
6 & Lagosanto & 0.0597 & 0.1319 & 0.0722 \\ \hline
7 & Poggio Renatico & 0.0523 & 0.167 & 0.1147 \\ \hline
8 & Argenta + Portomaggiore & 0.0307 & 0.1133 & 0.0826 \\ \hline
9 & Copparo & 0.0261 & 0.1107 & 0.0846 \\ \hline
10 & Bondeno & 0.0222 & 0.1075 & 0.0853 \\ \hline
11 & Comacchio & 0.0217 & 0.1075 & 0.0857 \\ \hline
12 & Codigoro & 0.0125 & 0.1053 & 0.0928 \\ \hline
13 & Formignana & \(-\)0.1232 & 0.0146 & 0.1378 \\ \hline
14 & Masi Torello & \(-\)0.1275 & 0.0086 & 0.1361 \\ \hline
15 & Goro & \(-\)0.1278 & 0.0106 & 0.1384 \\ \hline
16 & Mesola & \(-\)0.1317 & 0.0069 & 0.1386 \\ \hline
17 & Berra & \(-\)0.1383 & 0.0046 & 0.1429 \\ \hline
18 & Voghiera & \(-\)0.1383 & 0.0041 & 0.1424 \\ \hline
19 & Ro & \(-\)0.1385 & 0.004 & 0.1425 \\ \hline
20 & Fiscaglia & \(-\)0.1497 & 0.002 & 0.1517 \\ \hline
21 & Ostellato & \(-\)0.1839 & 0 & 0.1839 \\ \hline
22 & Jolanda di Savoia & \(-\)0.2014 & 0 & 0.2014 \\ \hline \end{tabular}
\end{table} 
Table 6: Ranking of alternatives for the linear preference function and std-mean method. With Scenario 1 based on the variation of the flood hazard weight, the ranking of the municipalities remains almost unchanged, as the multi-risk map is identical to that of Scenario 0. On the other hand, the maps change when Scenarios 2 and 3 are adopted, as shown in Figure 13a. More marked differences can be observed when the weight of the PGA (Figure 13b,c) is changed. By increasing the weight of the land-use criterion, an increase in Scenario 1 does not reflect evident changes in the multi-risk map (Figure 13d). On the other hand, changes in Scenarios 2 and 3 affect the multi-risk map. Looking back at the strategic building criterion, we observe differences in the risk map when the first change of Scenario 1 is applied, compared to Scenario 0 (Figure 13e), and more so with the last two increases of Scenario 2 (Figure 13f). For the criterion of population density, the first increase in the weight according to Scenario 1 does not affect the map (see Figure 14a),  
Figure 13: Weights sensitivity analysis, multi-risk maps; (**a**) flood hazard weight increase assuming Scenarios 2 or 3; (**b**) PGA weight increase assuming Scenario 1; (**c**) PGA weight increase assuming Scenario 2; (**d**) land use weight increase assuming Scenarios 2 or 3; (**e**) strategic buildings weight increase assuming Scenario 1; (**f**) strategic buildings weight increase assuming Scenarios 2 or 3.