Page 286 - Materials Chemistry, Second Edition

284 13. Multi-criteria decision-making after life cycle sustainability assessment under hybrid information

The radiuses of the weights of these three dimensions can be determined after solving pro-
gramming (Eq. 13.3), and they are 0.1366, 0.1366, and 0.1032, respectively. Then, the interval
weights of these three dimensions can be determined according to Eq. (13.29).
In a similar way, all the interval weights of the criteria in each dimension can be deter-
mined. The results are presented in Table 13.7.
The global weights of these eight criteria can be determined after the local weights of the
criteria in each dimension and the weights of the dimensions. Taking the global weight of the
overnight investment costs (EC 1 ) as an example (Table 13.8):
(13.44)
½ 0:1643 0:4375Š 0:3000 0:5000½ Š ¼ 0:0493 0:2188½ Š
Step 4: Determining the weighted normalized decision-making matrix. The data of
each cell in the weighted normalized decision-making matrix can be determined by

TABLE 13.7 The local weights of the criteria in each dimension.
EN EN 1 EN 2 EN 3 EN 4
BO 1 1 [24] [57]
OW [5 7] [5 7] [1 4] 1
Central weights 0.3964 0.3964 0.1436 0.0635
Radius 0.0291 0.0219 0.0400 0.0400
Interval Weights [0.3673 0.4255] [0.3673 0.4255] [0.1036 0.1836] [0.0235 0.1035]
0.2396
ξ ∗ ¼ 0:2396,CR ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 0:0799 < 0:10
Þ +1
5+7 + 1 45 + 7ð
2
EC EC 1 EC 2
BO [1 2] 1
OW 1 [1 2]
Central weights 0.4000 0.6000
Radius 0.1000 0.1000
Interval weights [0.3000 0.5000] [0.5000 0.7000]
∗
ξ ¼0, CR¼0<0.10
S S 1 S 2
BO 1 [2 3]
OW [2 3] 1
Central weights 0.7143 0.2857
Radius 0.0476 0.0476
Interval weights [0.6667 0.7619] [0.2381 0.3333]
∗
ξ ¼0, CR¼0<0.10