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Fuzzy MCDM for ranking the biofuels production pathways 327

Table 11.4 The weights of the nine criteria and the performances of the three pathways
for bioethanol production with respect to each criterion using fuzzy numbers

Relative
Wheat-based Corn-based Cassava-based importance
LCC (0.1,0.3,0.5) (0.3,0.5,0.7) (0.5,0.7,0.9) (0.9,1.0,1.0)
CC (0.1,0.3,0.5) (0.9,1.0,1.0) (0.5,0.7,0.9) (0.7,0.9,1.0)
TA (0,0.1,0.3) (0.7,0.9,1.0) (0.3,0.5,0.7) (0.5,0.7,0.9)
H.Tox (0.1,0.3,0.5) (0.9,1.0,1.0) (0.5,0.7,0.9) (0.3,0.5,0.7)
PMF (0,0,0.1) (0.9,1.0,1.0) (0.3,0.5,0.7) (0.3,0.5,0.7)
TM (0.5,0.7,0.9) (0.5,0.7,0.9) (0.3,0.5,0.7) (0.7,0.9,1.0)
SB (0.3,0.5,0.7) (0.3,0.5,0.7) (0.5,0.7,0.9) (0.1,0.3,0.5)
CED (0.3,0.5,0.7) (0.5,0.7,0.9) (0.7,0.9,1.0) (0.3,0.5,0.7)
FS (0,0,0.1) (0.1,0.3,0.5) (0.9,1.0,1.0) (0.5,0.7,0.9)

The linguistic terms presented in Table 11.3 can be transported into tri-
angular fuzzy numbers and the results are presented in Table 11.4. It is worth
pointing out that there are multiple different stakeholders/decision-makers
participating in the decision-making process, and different multicriteria
decision-making matrices were provided by them, the users can use the
average value of the alternatives with respect to each evaluation criterion
to determine the sustainability sequence of the alternative pathways for
bioethanol production.
After this, the ranking matrix with respect to each criterion can be deter-
mined according to Eqs. (11.12, 11.13). Taking the criterion-LCC as an
example, the data of wheat-, corn-, and cassava-based technologies with
respect to LCC are (0.1,0.3,0.5), (0.3,0.5,0.7), and (0.5,0.7,0.9), respec-
tively. These three triangular fuzzy numbers can be ranked according to
Eq. (11.10), and λ takes the value of 0.50 in this study, and the ranking
matrix with respect to LCC can be then determined, as presented in

12 3
Wheat based 0 0 1
LCC
φ (11.22)
Corn based 0 1 0
¼
Cassava based 1 0 0
Similarly, the ranking matrices with respect to the other eight criteria can
also be calculated determined, and the results are presented in Table 11.5.
Meanwhile, the fuzzy weights of these nine criteria can be defuzzied by
Eq. (11.16), and the results are presented in Table 11.6.