Page 409 - Biofuels for a More Sustainable Future

364 Biofuels for a More Sustainable Future

Step 1: Determine the intuitionistic fuzzy decision-making matrix
according to the opinions of different stakeholders/decision-makers (Ren
and Liang, 2017).
Assume that a total of K groups of decision-makers/stakeholders partici-
pate inassessing the m biofuel production pathways{A 1 ,A 2 , …,A m }byusing
the n criteria {C 1 ,C 2 , …,C n }, they were first asked to use extreme poor (EP),
very poor (VP), poor (P), medium poor (MP), fair (F), medium good (MG),
good(G),verygood(VG),andextremegood(EG)(aspresentedinTable13.1)
to rate the m alternative biofuel production pathways with respect to each of
the ncriteriafor sustainability,andthesenaturalwordscanbetransformedinto
intuitionistic fuzzy numbers according to Table 13.2.The decision-making
matrix by the kth decision-maker is presented in Eq. (13.16).

C 1 C 2 C n
x,k x,k x,k x,k x,k x,k x,k x,k x,k
A 1 μ , υ , π μ , υ , π ⋯ μ , υ , π
11 11 11 12 12 12 1n 1n 1n
x,k
x,k
x,k
x,k
k μ , υ , π x,k μ , υ , π x,k ⋯ μ , υ , π x,k
x,k
x,k
X ¼ A 2
21 21 21 22 22 22 2n 2n 2n
⋮ ⋮ ⋮ ⋱ ⋮
x,k x,k x,k x,k x,k x,k x,k x,k x,k
A m μ , υ , π m1 μ , υ , π m2 ⋯ μ , υ , π mn
m2
m2
m1
m1
mn
mn
(13.16)
k
where X represents the decision-making matrix determined by the kth
x, k x, k x, k
decision-makers, and (μ ij ,υ ij ,π ij ) represents the performance of the
ith biofuel production pathway with respect to the jth criterion by the
kth decision-maker.
Step 2: Determine the weights of the criteria for sustainability assessment
according to the opinions of different stakeholders/decision-makers.
Table 13.2 The linguistic variables and corresponding intuitionistic fuzzy numbers
(Zhang and Liu, 2011)
Linguistic terms Abbreviation Intuitionistic fuzzy numbers
Extreme poor (extreme low) EP (EL) (0.05,0.95,0.00)
Very poor (very low) VP (VL) (0.15,0.80,0.05)
Poor (low) P (L) (0.25,0.65,0.10)
Medium poor (medium low) MP (ML) (0.35,0.55,0.10)
Fair (medium) F (M) (0.50,0.40,0.10)
Medium good (medium high) MG (MH) (0.65,0.25,0.10)
Good (high) G (H) (0.75,0.15,0.10)
Very good (very high) VG (VH) (0.85,0.10,0.05)
Extreme good (extreme high) EG (EH) (0.95,0.05,0.00)