PSI - Issue 64

Raul Berto et al. / Procedia Structural Integrity 64 (2024) 1733–1742 1735 Raul Berto, Chiara Bedon, Andrea Mio, Alessandro Mazelli, Paolo Rosato / Structural Integrity Procedia 00 (2019) 000 – 000 3

Fig. 1. Drawings of the case-study historic Villa-

Fig. 2. Proposed strengthening solutions: (a) OSB and self-tapping screws, (b) CLT and self-tapping screws, (c) Light-Weight Concrete slab.

2.3. The multi-attribute procedure The adopted procedure, based on (Roy, 1968) and subsequent variations (Figueira et al., 2010; Frini and Ben Amor, 2019; Taherdoost and Madanchian, 2023), unfolds in several phases (Berto et al., 2024): 1. Analysis: evaluation of the performance of parameter , with respect to alternative , in different time horizons (short, medium, and long term, corresponding to 0, 15, and 50 years respectively) and calculation of the discounted analysis matrices × ′ ; 2. Evaluation: transformation of into the corresponding attributes using appropriate value functions; 3. Identification of preference relations; 4. Temporal aggregation. In (1), the evaluation of parameters requires that an expert accurately assesses the performance of the -th parameter for the alternative . To ensure that time is considered appropriately, a discount rate is used [ ′ ] . Step (2) involves transforming the parameters into attributes through appropriate value functions, which normalize the performance levels. The extreme values, 0 and 1, represent the worst and best performances for each attribute. In (3), the evaluation matrices [ ] are compiled for the three considered periods t . The outranking relations, and so the preference relations, require the estimation of a weight vector that defines the relative importance of different attributes (Simos, 1990; Figueira and Roy, 2002). For each time period and pair of alternatives ( , ) , the concordance index ( , ) is calculated as: