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A
¼
ð
. Similar computations are performed for the remaining criteria. The
results are presented in last two columns of Table
9
.
Next, the distance d
v
(.) of each alternative from the fuzzy positive ideal matrix
(A*) and fuzzy negative ideal matrix (A
9
;
9
;
9
Þ
) are computed using Eqs. (
12
)and(
13
).
For example, for alternative A1 and criteria C1,
−
A
Þ
the distances d
v
ð
A
1
;
and
A
Þ
d
v
ð
A
1
;
are computed as follows:
r
1
3
½
ð
A
Þ
¼
2
2
2
d
v
ð
A
1
;
:
:
Þ
þð
:
:
Þ
þð
:
Þ
:
0
333
0
333
4
407
0
333
9
0
333
¼
5
529
r
1
3
½
ð
A
Þ
¼
2
2
2
d
v
ð
A
1
;
0
:
333
9
Þ
þð
4
:
407
9
Þ
þð
9
9
Þ
¼
5
:
663
Likewise, we compute the distances for the remaining criteria for the three
alternatives. The results are shown in Table
10
.
Then, we compute the distances d
i
and d
i
using Eqs. (
12
) and (
13
). For
example, for alternative A1 and criteria C1, the distances d
i
and d
i
are given by:
d
i
¼
5
:
529
þ
5
:
257
þþ
5
:
358
¼
85
:
057
d
i
¼
5
:
663
þ
6
:
502
þþ
6
:
264
¼
101
:
802
Table 10 Distance d
v
(A
i
, A*) and d
v
(A
i
, A
−
) for alternatives
Criteria
d
−
(min)
d*(max)
A1
A2
A3
A1
A2
A3
C1
5.529
5.979
5.529
5.663
4.940
5.663
C2
5.257
4.020
5.300
6.502
6.953
6.389
C3
5.358
5.425
5.210
6.264
6.038
6.653
C4
5.700
4.349
5.423
5.777
6.147
6.144
C5
4.168
5.350
4.194
6.540
6.281
6.392
C6
5.807
4.062
5.331
5.066
6.333
5.921
C7
5.241
4.982
5.359
5.699
6.212
5.550
C8
1.587
5.014
5.025
7.640
6.851
6.758
C9
5.464
5.619
5.201
5.438
5.301
5.759
C10
5.331
1.554
5.244
5.921
7.745
6.070
C11
5.324
6.007
5.789
5.591
4.467
5.181
C12
2.696
3.811
5.656
6.745
6.442
4.718
C13
5.541
5.244
5.541
5.650
6.070
5.650
C14
6.266
4.060
3.950
3.773
5.972
6.140
C15
5.220
5.220
5.251
6.617
6.617
6.519
C16
5.210
4.077
5.251
6.653
6.753
6.519
C17
5.358
5.665
5.669
6.264
5.703
5.591
85.057
80.439
88.924
101.802
104.824
101.616
Σ
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