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328 Biofuels for a More Sustainable Future

Table 11.5 The ranking matrices with respect to the other eight criteria
CC 1 2 3 TA 1 2 3
Wheat-based 0 0 1 Wheat-based 0 0 1
Corn-based 1 0 0 Corn-based 1 0 0
Cassava-based 0 1 0 Cassava-based 0 1 0
H.Tox 1 2 3 PMF 1 2 3
Wheat-based 0 0 1 Wheat-based 0 0 1
Corn-based 1 0 0 Corn-based 1 0 0
Cassava-based 0 1 0 Cassava-based 0 1 0
TM 1 2 3 SB 1 2 3
Wheat-based 1 0 0 Wheat-based 0 1 0
Corn-based 1 0 0 Corn-based 0 1 0
Cassava-based 0 1 0 Cassava-based 1 0 0
CED 1 2 3 FS 1 2 3
Wheat-based 0 0 1 Wheat-based 0 0 1
Corn-based 0 1 0 Corn-based 0 1 0
Cassava-based 1 0 0 Cassava-based 1 0 0

Then, the weighted ranking matrix can be obtained by
Eqs. (11.14–11.16), as presented in Eq. (11.23).
1 2 3
Wheat based 0:1477 0:0506 0:8017
(11.23)
Corn based 0:5823 0:4177 0
R ¼
Cassava based 0:4177 0:5823 0
The final ranking matrix can be determined by the fuzzy linear 0–1 pro-
gramming according to Eqs. (11.17)–(11.21), as shown in Eq. (11.24).
MaxS ¼ 0:1477z 11 +0:0506z 12 +0:8017z 13 +0:5823z 21
+0:4177z 22 +0:4177z 31 +0:5823z 32
z it 2 0, 1g,i ¼ 1,2,3;j ¼ 1,2,3
f
z 11 + z 12 + z 13 ¼ 1
z 21 + z 22 + z 23 ¼ 1
z 31 + z 32 + z 33 ¼ 1
(11.24)
z 11 + z 21 + z 31 ¼ 1
z 12 + z 22 + z 32 ¼ 1
z 13 + z 23 + z 33 ¼ 1

z 11 z 12 z 13

Z ¼ z 21 z 22 z 23

z 31 z 32 z 33