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A multicriteria intuitionistic fuzzy group decision-making method 365

The decision-makers were asked to use the linguistic terms including
extreme low (low), very low (VL), low (L), medium low (ML), medium
(M), medium high (MH), high (H), very high (VH), and extreme high
(EH) (as presented in Table 13.2) to evaluate the relative importance of
the n criteria for sustainability, and these linguistic terms can be transformed
into intuitionistic fuzzy numbers. The weights of the n criteria determined
by the kth decision-maker are presented in Eq. (13.17).
k μ W,k , μ W,k , π W,k μ W,k , μ W,k , π W,k ⋯ μ W,k , μ W,k , π W,k

W ¼ 1 1 1 2 2 2 1 1 1
(13.17)
k
where W represents the weight vector determined by the kth decision-
W,k W,k W,k
maker, and (μ j ,μ j ,π j ) represents the weight of the jth criterion deter-
mined by the kth decision-maker.
Step 3: Determine the weighted intuitionistic fuzzy decision-making
matrix determined by each decision-maker. The weighted intuitionistic
fuzzy decision-making matrix determined by the kth decision-makers can
be determined by Eqs. (13.18), (13.19)

C 1 C 2 C n
y,k y,k y,k y,k y,k y,k y,k y,k y,k
μ , υ , π μ , υ , π ⋯ μ , υ , π
A 1 11 11 11 12 12 12 1n 1n 1n

k y,k y,k y,k y,k y,k y,k y,k y,k y,k
Y ¼ A 2 μ , υ , π 21 μ , υ , π 22 ⋯ μ , υ , π 2n
22
21
21
22
2n
2n
⋮ ⋮ ⋮ ⋱ ⋮

y,k
y,k
y,k
y,k
y,k
μ , υ , π y,k μ , υ , π y,k ⋯ μ , υ , π y,k
y,k
A m
m1 m1 m1 m2 m2 m2 mn mn mn
(13.18)

y,k
x,k
y,k
x,k
μ , υ , π y,k ¼ μ W,k , υ W,k , π W,k
μ , υ , π x,k
ij ij ij j j j ij ij ij

μ
υ
υ ,1 + υ
μ , υ
¼ μ W,k x,k W,k + υ x,k υ W,k x,k W,k x,k μ W,k x,k υ W,k υ x,k
j ij j ij j ij j ij j ij j ij
(13.19)
k
where Y represents the weighted decision-making matrix determined by
y,k
y,k
y,k
the kth decision-makers, and (μ ij ,υ ij ,π ij ) represents the data in cell (i,
j) in the weighted decision-making matrix.
Step 4: Determine the aggregated decision-making matrix.
The relative importance of the decision-makers can be rated according to
thelinguistictermsincludingveryimportant(VI),important(I),medium(M),
unimportant (U), and very unimportant (VU), and these linguistic variables
can be transformed into intuitionistic fuzzy numbers according to Table 13.3.