Page 196 - Materials Chemistry, Second Edition

194 9. Life cycle decision support framework: Method and case study

Min 0:3 ξ +0:7 ξð 1 2 Þ
8
ξ u 2 l 1 2:49 u 2 ξ u 2
> 1 1
>
>
>
>
> ξ m 2 m 1 2:84 m 2 ξ m 2
1
1
>
>
>
>
> ξ l 2 u 1 3:2 l 2 ξ l 2
> 1 1
>
>
>
> ξ u 3 l 1 2:1 u 3 ξ u 3
> 1 1
>
>
>
>
> ξ m 3 m 1 2:52 m 3 ξ m 3
1
1
>
>
>
>
> ξ l 3 u 1 2:94 l 3 ξ l 3
> 1 1
>
>
>
>
1
1
> ξ u 2 l 1 2:49 u 2 ξ u 2
>
>
>
>
> ξ m 2 m 1 2:84 m 2 ξ m 2
1
1
>
>
>
>
>
> ξ l 2 u 1 3:2 l 2 ξ l 2
1
1
>
>
>
>
> ξ u 2 l 3 0:47 u 2 ξ u 2
1
1
>
>
>
>
>
1
1
> ξ m 2 m 3 0:71 m 2 ξ m 2
>
>
>
>
> ξ l 2 u 3 0:82 l 2 ξ l 2
1
1
>
>
>
>
>
> ξ u 2 l 1 2:49 u 2 ξ u 2
2
2
>
>
>
>
> ξ m 2 m 1 2:84 m 2 ξ m 2
2
2
< (9.8)
s:t:
ξ l 2 u 1 3:2 l 2 ξ l 2
2
2
>
>
>
>
> ξ u 3 l 1 2:1 u 3 ξ u 3
2
2
>
>
>
>
> ξ m 3 m 1 2:52 m 3 ξ m 3
> 2 2
>
>
>
>
> ξ l 3 u 1 2:94 l 3 ξ l 3
2
2
>
>
>
>
> ξ u 1 l 2 2:49 u 1 ξ u 1
> 2 2
>
>
>
>
> ξ m 1 m 2 2:84 m 1 ξ m 1
2
2
>
>
>
>
>
2
2
> ξ l 1 u 2 3:2 l 1 ξ l 1
>
>
>
>
> ξ u 1 l 3 0:47 u 1 ξ u 1
2
2
>
>
>
>
>
2
2
> ξ m 1 m 3 0:71 m 1 ξ m 1
>
>
>
>
> ξ l 1 u 3 0:82 l 1 ξ l 1
2
2
>
>
>
>
> ð l 1 +4 m 1 + u 1 Þ ð l 2 +4 m 2 + u 2 Þ ð l 3 +4 m 3 + u 3 Þ
>
> + + ¼ 1
>
> 6 6 6
>
>
>
>
> 0 l 1 m 1 u 1
>
>
>
>
>
> 0 l 2 m 2 u 2
>
>
:
0 l 3 m 3 u 3
The local fuzzy weights for environmental, economic, and social perspectives, respec-
tively, can be calculated by Eq. (9.8) as e w en ¼ 0:2304, 0:2304, 0:2304ð Þ, e w ec ¼
ð 0:4863, 0:5676, 0:6499Þ, and e w so ¼ 0:1958, 0:1958, 0:2320ð Þ. According to Eq. (9.4), the crisp
local weights for those three perspectives were calculated as w en ¼0.2304, w ec ¼0.5678, and
w so ¼0.2018. Similarly, the local weights for environmental criteria, economic criteria, and