PSI - Issue 64

1736 Raul Berto et al. / Procedia Structural Integrity 64 (2024) 1733–1742 4 Raul Berto, Chiara Bedon, Andrea Mio, Alessandro Mazelli, Paolo Rosato / Structural Integrity Procedia 00 (2019) 000 – 000 ( , )=∑ :∆≥0 (1) with ∆= − , where represents the state of the -th attribute of the -th alternative, and represent the state of the -th attribute of the -th alternative. The discordance index ( , ) for each pair of alternatives ( , ) and for each period is then calculated as: ( , )= max :∆<0 (|∆|× ) max (|∆|× ) (2) Starting from the calculated concordance and discordance indices, the outranking relations ( , ) for each pair of alternatives ( , ) for each period can be determined. Considering three concordance thresholds 1 > 2 > 3 and two discordance thresholds 1 > 2 we have that in period if ( , ) = : ( ∑ : > ∑ : < ) > 1 { ( , )≥ 1 ( , )≤ 2 (3) or ( ∑ : > ∑ : < ) > 1 { ( , )≥ 2 ( , )≤ 1 (4) and in period if ( , ) = : ( ∑ : > ∑ : < ) > 1 ( , )≥ 3 ( , )≤ 2 (5) Then, for each period and for each pair ( , ) , the corresponding preference relation ( , ) is determined, where ( , ) ∈ ( , , , , −1 , −1 ) . is strict preference, the weak preference, the indifference, the incomparability, −1 is the inverse of weak preference, and −1 is the inverse of strict preference. The phase (4) involves the temporal aggregation of evaluations for each period . For each pair ( , ) and period , the distance between preference relations ( , ) with every possible binary relation ∈ ( , , , , −1 , −1 ) is determined with ∆ ( , ( , )) , see Table 1 (Frini and Ben Amor, 2019; Ben Amor and Martel, 2014). The distances obtained for each period are aggregated into an average distance ∆̅ ( , ( , )) . For each pair ( , ) , the preference relation ∗ is assigned, where H* corresponds to the preference relation associated with the minimum value of the calculated average distances. Table 1.The distance measures between preference relations. Binary relations I Q P R Q -1 P -1 I 0.000 1.000 1.263 1.579 1.000 1.263 Q 1.000 0.000 1.000 1.579 1.474 1.895 P 1.263 1.000 0.000 1.579 1.895 2.000 R 1.579 1.579 1.579 0.000 1.579 1.579 Q -1 1.000 1.474 1.895 1.579 0.000 1.000 P -1 1.263 1.895 2.000 1.579 1.000 0.000

3. Calculation and results 3.1. Analysis

Economic parameters: An analytical approach was adopted to estimate the implementation costs of interventions ( =0 ) and decommissioning ( =50 ), based on unit prices in the Regional Public Works Price List of the Friuli Venezia Giulia region (2023), see Table 2. Architectural parameters : A building reuse expert was interviewed. The expert assigned a 0-10 score to each parameter (0 = worst, 10 = best performance), considering constant performances for different times (Table 3).