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A multicriteria intuitionistic fuzzy group decision-making method 367

Step 5: Determine the ideal and antiideal intuitionistic fuzzy solutions.
The ideal and antiideal intuitionistic fuzzy solutions after determining the
aggregated decision-making matrix according to Xu (2007b), as presented
in Eqs. (13.23)–(13.26).
+
+
+

A ¼ a , a , …, a n + (13.23)
2
1
m m
m
m
y
y
y
a ¼ max μ , min υ ,1 max μ min υ y (13.24)
+
j i1 i1 i1 i1
i¼1 i¼1 i¼1 i¼1

A ¼ a , a , …, a (13.25)

1 2 n

m m m m
y
y
y
a ¼ min μ , max υ ,1 min μ max υ y (13.26)

j i1 i1 i1 i1
i¼1 i¼1 i¼1 i¼1
Step 6: Determine the degree of the similarity of each alternative and the
ideal intuitionistic fuzzy solution and that of each alternative and the anti-
ideal intuitionistic fuzzy solution.
The degree of the similarity of each alternative and the ideal intuitionistic
fuzzy solution and that of each alternative and the antiideal intuitionistic
fuzzy solution can be determined by Eqs. (13.27), (13.28).
+
SA i , Að Þ ¼ 1
!3 1
2
n 2 m 2 m 2 2
m
m
y
y
y
y
μ max μ y + υ min υ + π 1 max μ min υ y

X

y

6 ij ij ij ij i1 7
i¼1 ij i¼1 i¼1 i¼1 i1
6 7
j¼1
6 7
n 2 !7
6
6 X y m y y m 2 y m y m y 2 7

y
4 μ + max μ + υ + min υ + π +1 max μ min υ 5
ij ij ij ij i1
i¼1 ij i¼1 i¼1 i¼1 i1
j¼1
(13.27)
Þ ¼ 1

SA i , Að !3 1
2
n 2 2 2 2
X m m m m
μ min μ + υ max υ + π 1 min μ max υ
y y y y y y y
6 ij ij ij ij i1 7
ij i1
6 i¼1 i¼1 i¼1 i¼1 7
j¼1
6 7
n 2 2
6 !7
X m m 2 7
6 y y m y y y m y
μ + min μ + υ + max υ + π +1 min μ max υ
y
4 5
ij i¼1 ij ij i¼1 ij ij i¼1 i1 i¼1 i1
j¼1
(13.28)
+
where S(A i ,A ) and S(A i ,A ) represent the similarity of the jth alternative

and the ideal intuitionistic fuzzy solution and that of the jth alternative and
the antiideal intuitionistic fuzzy solution.
Step 7: Determine the relative similarity measure of each alternative and
rank the alternatives.
The relative similarity measure of the ith alternative can be determined
by Eq. (13.29) (Xu, 2007b).