PSI - Issue 64

Raul Berto et al. / Procedia Structural Integrity 64 (2024) 1733–1742 1739 Raul Berto, Chiara Bedon, Andrea Mio, Alessandro Mazelli, Paolo Rosato / Structural Integrity Procedia 00 (2019) 000 – 000 7

3.2 Evaluation For the transformation, synthesis, and normalization of parameters into attributes, linear monotonic value functions were adopted on a 0-1 scale. For economic, environmental, architectural and structural parameters, 1 corresponds to the preferred situation, and 0 to the highest value (1-min / 0-max). The evaluation matrices are in Table 9. Table 9. Evaluation matrices. =0 =15 =50 Value function OSB CLT LWC OSB CLT LWC OSB CLT LWC Implementation cost 1.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1-min / 0-max Decommissioning cost 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.84 0.00 1-min / 0-max GWP 1.00 0.62 0.00 1.00 1.00 1.00 0.00 1.00 0.30 1-min / 0-max Water use 1.00 0.31 0.00 1.00 1.00 1.00 1.00 0.64 0.00 1-min / 0-max Reversibility 1.00 1.00 0.00 1.00 1.00 0.00 1.00 1.00 0.00 1-max / 0-min Invasiveness 0.71 1.00 0.00 0.71 1.00 0.00 0.71 1.00 0.00 1-max / 0-min Δ SLS 0.00 0.56 1.00 0.00 0.68 1.00 0.00 0.68 1.00 1-max / 0-min Δ ULS 0.03 0.00 1.00 0.04 0.00 1.00 0.00 0.06 1.00 1-max / 0-min Δ DL 0.05 0.00 1.00 0.00 0.92 1.00 0.00 0.92 1.00 1-max / 0-min Δ LS 0.00 0.67 1.00 0.00 0.26 1.00 0.00 0.26 1.00 1-max / 0-min 3.3 The preference relations The weighting of individual attributes (Simos, 1990;Figueira and Roy, 2002) assumes that the ratio between the most and least important attribute is 2 (Table 10). The definition of thresholds is: c 1 =0.8; c 2 =0.7; c 3 =0.6; d 1 =0.2; d 2 =0.5. Then, the preference relations are shown in Table 11. Table 10 . The attributes’ weights. Implementation cost 3.57% GWP 14.29% Reversibility 17.86% Δ SLS 7.14% Δ DL 7.14% Decommissioning cost 3.57% Water use 14.29% Invasiveness 17.86% Δ ULS 7.14% Δ LS 7.14% Table 11. Preference relations. =0 =15 =50 0 ( , ) 0 ( , ) Preference relation 15 ( , ) 15 ( , ) Preference relation 50 ( , ) 50 ( , ) Preference relation OSB vs CLT 0.68 0.52 R 0.61 1 P -1 0.39 1 P -1 CLT vs OSB 0.54 1 R 0.93 0.04 P 0.82 0.36 P OSB vs LWC 0.71 0.4 Q 0.71 0.4 Q 0.57 0.4 R LWC vs OSB 0.32 1 Q -1 0.64 1 Q -1+ 0.46 1 R CLT vs LWC 0.68 0.4 Q 0.71 0.4 Q 0.71 0.38 Q LWC vs CLT 0.32 1 Q -1 0.64 1 Q -1 0.32 1 Q -1 3.4 Temporal aggregation Table 12 is an example of temporally aggregated preference relation for OSB vs CLT pair. By adopting the same procedure, the temporally aggregated preference relations are shown in Table 13 and Fig. 3 .

Table 12. The preference relation for OSB vs CLT.

OSB vs CLT 0 ( , )= 1.579 1.579 1.579 0 1.579 1.579 15 ( , )= −1 1.263 1.895 2 1.579 1 0 50 ( , )= −1 1.263 1.895 2 1.579 1 0 I Q P R Q -1 P -1