Page 284 - Materials Chemistry, Second Edition

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

TABLE 13.4 The normalized decision-making matrix.
Coal Oil Biomass Ocean Wind
[0.2860 2.2190] [0.7352 0.7352] [0.1798 0.5343] [0.2102 0.4193] [0.3595 1.0922]
EC 1
EC 2 [0.5869 2.0275] [0.6560 0.6560] [0.3396 1.0620] [0.1928 0.2987] [0.2859 0.9558]
EN 1 [0.0115 0.0157] [0.1357 0.3733] [0.0385 0.8783] [0.2986 1.8664] [0.2715 1.8664]
EN 2 [0.0088 0.1376] [0.0138 0.0481] [0.1204 0.4814] [2.4072 2.4072] [0.3210 1.9257]
EN 3 [0.0123 0.0247] [0.0154 0.0411] [0.1121 1.2336] [2.4671 2.4671] [0.3084 1.2336]
EN 4 [0.0341 0.2047] [0.0930 0.4094] [0.0341 0.2924] [2.0468 2.0468] [0.5117 2.0468]
S 1 [0.4034 0.5665] [0.9054 1.0201] [1.0544 1.1232] [1.1324 1.1444] [1.1438 1.1458]
S 2 [1.0259 1.0268] [1.0248 1.0266] [1.0228 1.0264] [0.8420 0.9447] [0.9242 0.9755]

respect to these six cost-type criteria can be normalized by Eqs. (13.21), (13.22). The results are
presented in Table 13.4.
Step 3: Determining the weights of the three dimensions of sustainability and the local
weights of the criteria in each dimension. Taking the three dimensions of sustainability as an ex-
ample, the environmental dimension and the social dimension were recognized as the most im-
portant and the least important, respectively. The BO and the OW are presented in Table 13.5.
Based on the BO and OW vectors, the following programming model was established for
determining the central weights of these three dimensions:

minξ
s:t:
ω
C
1+ 3
EN
ξ
ω C
2
EC
ω
C
EN
3+ 6
ξ
ω C
S 2
ω
C (13.41)
2+ 3
EC
ξ
ω C 2
S
ω C + ω C + ω ¼ 1
C
EC EN S
ω C 0
EC
C
ω 0
N
C
ω 0
S
TABLE 13.5 The BO and OW vectors for determining the weights of
economic, environmental, and social dimensions.
Economic Environmental Social
BO [1 3] 1 [3 6]
OW [2 3] [3 6] 1