## 7 Introduction of the Information Quality (IQ) Index  
The individual building's vulnerability is influenced by the knowledge of the uncertainties related to considered parameters; the procedure before presented was therefore repeated introducing an _Information Quality_ (IQ) index accounting for confidence level (CL) classes defined for the different parameters used in the I\({}_{\text{V}}\) method. A 4-level confidence scale was developed based on the experience gained during the damage survey:  
* _High confidence level_ (H): high information quality coming from complete (internal and external) surveys and direct measures on buildings including structures, materials, details, etc. High confidence in achieved data. * _Medium confidence level_ (M): medium information quality, coming from external surveys on buildings and information rescued from historical/critical analysis or visual inspections. Medium confidence in achieved data resulted from direct/indirect measurements. * _Low confidence level_ (L): external geometrical survey of the construction through satellite images integrated with considerations coming from buildings of similar typologies. Very low confidence in achieved data resulted from hypotheses not verified for the building or the urban setting. _Absent confidence level_ (A): information adopted with limited confidence or by random choice. The parameters' class attribution is only indicative. Three additional intermediate categories were introduced, with the aim of reducing the arbitrary choices of a class and providing an improved score assignment [45]: high-medium (HM), medium-low (ML) and low-absent (LA). The definition of a large number of confidence classes was related to the specific features of the constructions, characterized by high variability, and by the experience of the surveyor, that--as said--highly influences the outputs of I\({}_{\text{V}}\) methods. Figure 19 shows the distribution of the CL in the case study; thanks to the different information collected and inspections carried out, more than 66% of the parameters resulted in a high-medium CL. In relation to assessed CL, a coefficient accounting for related uncertainties (UL) was determined (Table 8). The final CL for each class then resulted from the weighted average of the different CL ranges assigned to the buildings, neglecting the extreme cases with damage equal to D0-D1 or D5 according to EMS98 classification. The level of uncertainty (UL) was applied to the weight of each parameter, determining the relevance (\(\Delta\)) of the parameter for the seismic behaviour of the building, Equation (11). \[\Delta=\frac{\sum\mathrm{P_{i}\cdot UL}}{\sum\mathrm{P_{i}}} \tag{11}\]  
being \(p_{i}\) the weight of the i-th parameter and UL the corresponding uncertainty in relation to Table 8. The \(\Delta\) value was used to increase or reduce the \(\mathrm{I_{V}}\) defining a range where the vulnerability index expresses a correct result (11). These bounds can be seen as the transposition of the percentage of uncertainty coming from the evaluation of the parameters determining the \(\mathrm{I_{V}}\). The range of numbers associated to each class was evaluated by checking whether the average of the damage detected \((\overline{\mu_{R}})\) was within the upper \(\left(\mu_{T}^{+}\right)\) and lower bound \(\left(\mu_{T}^{-}\right)\) of the theoretical damage, assessed by increasing and reducing the \(\mathrm{I_{V}}\). The definition of the CL to be assigned to each class was defined through a step-by-step procedure, in which the uncertainty interval was calculated after assessing the vulnerability of each building (Figure 20). \[\mathrm{I_{V}}\ =\left\{ \begin{array}{c}\mathrm{I_{V}^{-}=\sum\mathrm{P_{i}}(1- \Delta)\cdot c_{i}\rightarrow\mu_{T}^{-}\ (lower\ bound)}\\ \overline{\mathrm{I_{V}}}=\sum\mathrm{P_{i}\cdot c_{i}\rightarrow\overline{ \mu_{T}}}\\ \mathrm{I_{V}^{+}=\sum\mathrm{P_{i}}(1+\Delta)\cdot c_{i}\rightarrow\mu_{T}^{+ }\ (upper\ bound)}\end{array} \right. \tag{12}\]