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Table 6 Aggregate fuzzy weights for 17 criteria
Criteria
Decision makers
Aggregate fuzzy weight
D1
D2
D3
C1
(5, 7, 9)
(3, 5, 7)
(7, 9, 9)
(3, 7, 9)
C2
(1, 1, 3)
(7, 9, 9)
(1, 3, 5)
(1, 4.334, 9)
C3
(1, 3, 5)
(1, 3, 5)
(7, 9, 9)
(1, 5, 9)
C4
(1, 1, 3)
(5, 7, 9)
(7, 9, 9)
(1, 5.667, 9)
C5
(1, 1, 3)
(3, 5, 7)
(5, 7, 9)
(1, 4.334, 9)
C6
(3, 5, 7)
(7, 9, 9)
(3, 5, 7)
(3, 6.334, 9)
C7
(5, 7, 9)
(5, 7, 9)
(5, 7, 9)
(5, 7, 9)
C8
(3, 5, 7)
(3, 5, 7)
(5, 7, 9)
(3, 5.667, 9)
C9
(7, 9, 9)
(5, 7, 9)
(5, 7, 9)
(5, 7.667, 9)
C10
(3, 5, 7)
(5, 7, 9)
(5, 7, 9)
(3, 6.334, 9)
C11
(7, 9, 9)
(5, 7, 9)
(5, 7, 9)
(5, 7.667, 9)
C12
(7, 9, 9)
(5, 7, 9)
(5, 7, 9)
(5, 7.667, 9)
C13
(3, 5, 7)
(7, 9, 9)
(3, 5, 7)
(3, 6.334, 9)
C14
(5, 7, 9)
(5, 7, 9)
(5, 7, 9)
(5, 7, 9)
C15
(1, 3, 5)
(5, 7, 9)
(1, 1, 3)
(1, 3.667, 9)
C16
(3, 5, 7)
(1, 1, 3)
(7, 9, 9)
(1, 5, 9)
C17
(5, 7, 9)
(3, 5, 7)
(1, 3, 5)
(1, 5, 9)
Likewise, the aggregate ratings for the alternatives (A1, A2, A3) with respect to
the 17 criteria are computed. The aggregate fuzzy decision matrix for the alterna-
tives is presented in Table
7
.
Then, normalization of the fuzzy decision matrix of alternatives is performed
using Eqs. (
6
), (
7
) and (
8
). For example, the normalized rating for alternative A1 for
criteria C1 is given by:
c
j
¼
max
i
ð
9
;
9
;
9
Þ
¼
9
a
j
¼
mini
i
ð
1
;
3
;
1
Þ
¼
1
Since C1 is a bene
t (B) category criteria,
1
9
;
5
:
667
9
9
9
Þ
¼
ð
r
ij
¼
ð
;
0
:
111
;
0
:
629
;
1
Þ
Likewise, the normalized values of the three alternatives with respect to the 17
criteria are computed. The value of a
j
¼
1 and c
j
¼
9 for all criteria. The nor-
malized fuzzy decision matrix for the three alternatives is presented in Table
8
.
Next, the fuzzy weighted decision matrix for the three alternatives is constructed
using Eq. (
9
). The
~
r
ij
values from Table
8
and
w
j
values from Table
6
are used to
~
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