## 3 Quantification, Assessment, and 3D Visualisation of UES in Naples
### Multi-Criteria Decision Analysis through the Spatial AHP Method  
The aggregation rule of the spatial AHP method, implemented into the Multi-Criteria Analytical Scoring Tool (MASCOT) software [99], allowed us to produce a normalised index of UES per cell, using pairwise-compared indicators and the Euclidean distance method, referring to the DTM. The enhancement offered by the tool consists of the two-fold processing of the cell-by-cell weighted sum and the Euclidean distance among spatial elements. The number of objects within the DTM and their weighted sum provide the overall UES score per cell. Finally, UES indicator values can be standardised within the range of 0-1 using the Min-Max formula (1):  
\[I_{i,k}=\frac{a_{ik}-min_{i}\ \{a_{ik}\}}{max_{i}\ \{a_{ik}\}-min_{i}\ \{a_{ik}\}} \tag{1}\]  
where \(a_{ik}\) is the indicator value per cell and \(I_{ik}\) is the normalized indicator.  
The four operational steps for performing the spatial MCDA in the MASCOT software are as follows:  
1. Bundling tiers in three thematic groups, referring to the Regulation, Carrier, and Information macro-categories;
2. Choosing the DT per criterion/tier (the DT determines the maximum weight for a cell touched by a tier; the weight decreases linearly, down to zero at the boundaries of the setting distance);
3. Weighting tiers through AHP pairwise comparisons at three levels (in this application, the Equal Weights method was used);
4. Scoring tiers with the weighted sum, in order to derive the overall results for each macro-category.  
In particular, the weighting phase was performed by the attribution of judgments--with the 9-point \"Saaty semantic scale\"--at hierarchical levels referring to three bundles of pairwise comparison matrices. At the \"macro-category\" level, a matrix (\(3\times 3\)) was filled. The \"categories\" level includes three square matrices:  
* A matrix (\(5\times 5\)) for tiers within the Regulation Services \"macro-category\";
* A matrix (\(9\times 9\)) for tiers within the Carrier Services \"macro-category\";
* A matrix (\(6\times 6\)) for tiers within the Information Services \"macro-category\".  
At the last level, the \"sub-categories\" include fine-grained information related to some elements of the top categories. The \"sub-categories\" level contains:  
* A matrix (\(2\times 2\)) within the \"Environmental protection area\" category, which includes SIC and ZPS as polygonal items;
* A matrix (\(4\times 4\)) within the \"Waterway\" category, which includes streams, drains, docks, and canals as polygonal items;
* A matrix (\(14\times 14\)) within the \"Railway\" category, which includes yards, turntables, trams, subways, stations, rails, platforms, funcilvars, monorails, narrow-gauge lines, abandoned lines, construction lines, disused lines, and light-rails as linear items;
* A matrix (\(10\times 10\)) within the \"Roads\" category, which includes bridleways, cycleways, footways, motorways, pedestrian ways, pathways, steps, secondary roads, trunks, and tracks as linear items;
* A matrix (\(2\times 2\)) within the \"Bus/underground stop\" category;
* A matrix (\(4\times 4\)) within the \"Tourism facility\" category, which includes hotels, hostels, guest-houses, and campsites as point items;
* A matrix (\(4\times 4\)) within the \"Attraction place\" category, which includes theatres, cinemas, and observatories as point items.  
The AHP procedures allow for calculating weights, through formulas (2) and (3) [77; 99]:  
\[W_{i}=\frac{M_{i}}{\sum_{K=1}^{N}M_{k}}, \tag{2}\]  
\[M_{i}=\sqrt[N]{\prod_{j=i}^{N}A_{ij}} \tag{3}\]  
where \(W_{i}\) is the weight of the \(i^{\text{th}}\) criterion and \(A_{ij}\) represents the pairwise comparison matrices. The scoring cell derives from the multiplication of weights at each hierarchical level, while the weighted sum of each contribution determines the overall UES score per cell.