Page 391 - Biofuels for a More Sustainable Future

Prioritization of biofuels production pathways under uncertainties 347

⋯

C 1 C 2 C n

A 1 ω r ω r ⋯ ω r

1 11 2 12
n 1n
¼ A 2 ω r ω r ⋮ ω r

V ¼ v ij 1 21 2 22 (12.20)
m n n 2n
⋮ ⋮ ⋯ ⋱ ⋮

A m ω r ω r ⋯ ω r

1 m1 2 m2 n mn
where ω 1 represents the interval weight of the jth criterion determined by

the interval AHP method.
Step 4: Determining the reference series. The reference series (RS)
h i
v
v RS ¼ v RS RS + , j ¼ 1,2,…,n can be determined by
j
j
j
Eqs. (12.21)–(12.23).

RS ¼ v RS , v RS , …, v RS (12.21)
1 2 n
+
v RS + max v , j ¼ 1,2,…,n (12.22)
j ¼ ij
i¼1,2,…,m
v RS max v , j ¼ 1,2,…,n (12.23)

j ¼ ij
i¼1,2,…,m
Step 5: Calculating the correlation coefficients of the series of each alter-
native to the reference series with respect to each criterion. ρ takes the value
of 0.5 in this study.

min mindv , v RS + ρmax maxdv , v RS

ij
j
j
ij
i j i j
i (12.24)
ξ j ðÞ ¼
dv , v RS + ρmax maxdv , v RS

ij j ij j
i j
RS RS , and it can be
d(v ij ,v j ) represents the distance between v ij and v j
determined according to the work of Wang et al. (2017).
Step 6: Determining the correlation degree of the series of each alterna-
tive to the reference series.
n
X
ξ ,i ¼ 1,2,…,m (12.25)
r i ¼ ij
j¼1
After determining the correlation degree of the series of each alterna-
tive to the reference series, the priority sequence of the alternatives can be
determined according to the rule that the greater the value of r i ,the more
superior the alternative will be. Accordingly, the greater the value of r i ,the
more sustainable the corresponding pathway for biofuel production
will be.