Information Technology Reference
In-Depth Information
A ¼ ð~
v 1 ; ~
v 2 ; ...; ~
v n Þ
v j ¼
where
~
max
i
f
v ij3 g;
i
¼
1
;
2
; ...;
m
;
j
¼
1
;
2
; ...;
n
ð 10 Þ
A ¼ ð v 1 ; v 2 ; ...; v n Þ
v j ¼
where
mini
i
f v ij1 g; i ¼
1
;
2
; ...; m ; j ¼
1
;
2
; ...; n
ð 11 Þ
Step 7: Compute the distance of each alternative from FPIS and FNIS:
The distance (d i , d i ) of each weighted alternative i
¼
1
;
2
; ...;
m from the FPIS
and the FNIS is computed as follows:
X
n
d i ¼
d v ð v ij ; v j Þ;
i
¼
1
;
2
; ...;
m
ð 12 Þ
j¼1
X
n
d i ¼
v j
d v ð~
v ij ; ~
Þ;
i
¼
1
;
2
; ...;
m
ð 13 Þ
j¼1
r
1
3
h
i
where d ð a ; b Þ ¼
2
2
2
ð a 1 b 1 Þ
þð a 2 b 2 Þ
þð a 3 b 3 Þ
is the distance mea-
surement between two fuzzy numbers a and b.
Step 8: Compute the closeness coef
cient (CCi) i ) of each alternative.
The closeness coef
cient CCi i represents the distances to the fuzzy positive ideal
solution (A*) and the fuzzy negative ideal solution (A
) simultaneously. The
closeness coef
cient of each alternative is calculated as:
d i
d i þ
CC i ¼
d i ;
i
¼
1
;
2
; ...;
m
ð 14 Þ
Step 9: Rank the alternatives
In step 9, the different alternatives are ranked according to the closeness coef
cient
(CC i ) in decreasing order. The best alternative is closest to the FPIS and farthest
from the FNIS.
3.3 Sensitivity Analysis
The third step involves conducting the sensitivity analysis. Sensitivity analysis
addresses the question,
How sensitive is the overall decision to small changes in
the individual weights assigned during the pair-wise comparison process?
. This
question can be answered by varying slightly the values of the weights and
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