## 3 Proposed Methodological Approach
### Electre Tri  
After weighting criteria via DEMATEL, we propose the use of the ELECTRE TRI method to sort alternatives (measures) into ordered classes, each class reflecting a different level of priority suggested for the implementation of measures. ELECTRE TRI can be implemented by means of two phases [37]. The first phase aims to build outranking relations between pairs of alternatives on the basis of concordance and discordance criteria. These relations are manipulated during the second phase of the procedure, aiming at sorting alternatives to different classes according to their shared characteristics. The mentioned sorting procedure is developed by means of two different approaches that will be discussed later, which are a pessimistic assignment and an optimistic assignment. We begin by collecting the input data required for the methodological implementation: criteria \(B_{k}\) or aspects mostly relevant to the decision-making problem under analysis; criteria weights \(w_{k}\); reference profiles delimiting classes \(P_{j}\), each profile being defined by two limits \(p_{h}\) and \(p_{h+1}\); classes \(C_{h}\) where alternatives will be sorted; alternatives \(A_{i}\); quantitative evaluations of alternatives under criteria \(B_{k}(A_{i})\); threshold value, or cutting level, \(\lambda\) ranged within \([0.5,1]\); thresholds of indifference \(I_{k}\), strong preference \(S_{k}\) and veto \(V_{k}\), to be defined to characterize the specific outranking relations among alternatives. These three thresholds need to be set for each criterion by implementing a trial-and-error process, where the analyst makes attempts to determine the most appropriate numerical values [31]. \(I_{k}\) stands for the minimum difference necessary to indicate preference between a pair of alternatives under a given criterion, \(S_{k}\) signifies the minimum difference required to assert strong preference between a pair of alternatives, and \(V_{k}\) denotes the minimum difference highlighting an incompatibility relation between a pair of elements [38]. We report in the following a brief recall about how to implement the steps for carrying out the first phase of the ELECTRE TRI procedure. * Computing, for each criterion \(B_{k}\), suitable partial concordance indices by pairwise comparing each alternative \(A_{i}\) with reference profiles \(P_{j}\). Concordance indices \(C_{k}(A_{i},P_{j})\) are obtained as follows: \[C_{k}(A_{i},P_{j})= \begin{cases}1\quad if\quad\left[B_{k}(P_{j})-B_{k}(A_{i} )\right]\leq I_{k}\\ 0\quad if\quad\left[B_{k}(P_{j})-B_{k}(A_{i})\right]\geq S_{k}.\\ \frac{B_{k}(A_{i})-B_{k}(P_{j})+S_{k}}{S_{k}-I_{k}}\quad\text{otherwise}\end{cases} \] (3) Once partial concordance indices have been obtained for each criterion, they are merged into the aggregated concordance index \(C(A_{i},P_{j})\) via the following equation: \[C(A_{i},P_{j})=\frac{\sum_{k=1}^{K}w_{k}\cdot C_{k}(A_{i},P_{j})}{\sum_{k=1}^ {K}w_{k}}.\] (4)
* Computing, for each criterion \(B_{k}\), suitable partial discordance indices by pairwise comparing each alternative \(A_{i}\) with reference profiles \(P_{j}\). Discordance indices \(D_{k}(A_{i},P_{j})\) are obtained as follows: \[D_{k}(A_{i},P_{j})= \begin{cases}1\quad if\quad\left[B_{k}(P_{j})-B_{k}(A_{i} )\right]>V_{k}\\ 0\quad if\quad\left[B_{k}(P_{j})-B_{k}(A_{i})\right]\leq S_{k}.\\ \frac{B_{k}(P_{j})-B_{k}(A_{i})-S_{k}}{V_{k}-S_{k}}\quad\text{otherwise}\end{cases} \] (5)
* Computing the outranking credibility index, which assesses the credibility of outranking relationships between alternatives. This index measures the extent to which an alternative outranks another in terms of meeting the criteria specified in the decision-making process. It can be calculated by implementing the following formula: \[\delta(A_{i},P_{j})=C(A_{i},P_{j})\cdot\frac{\prod_{k\in K^{*}}(1-D_{k}(A_{i},P_{j}))}{1-C(A_{i},P_{j})},\] (6) where \(K^{*}\) is the subset of criteria for which \(D_{k}(A_{i},P_{j})>C(A_{i},P_{j})\).