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Since
Z
2
=
Z
, then
Z
is not an intuitionistic fuzzy equivalence matrix. Thus we need
to calculate
Z
4
Z
2
Z
2
=
◦
⎛
⎞
(
1
,
0
)
(
0
.
78
,
0
.
08
)(
0
.
78
,
0
.
08
)(
0
.
71
,
0
)(
0
.
71
,
0
.
08
)
⎝
⎠
(
0
.
78
,
0
.
08
)
(
1
,
0
)
(
0
.
78
,
0
.
08
)(
0
.
71
,
0
.
08
)(
0
.
71
,
0
)
Z
2
(
0
.
78
,
0
.
08
)(
0
.
78
,
0
.
08
)
(
1
,
0
)
(
0
.
71
,
0
.
08
)(
0
.
71
,
0
.
08
)
=
=
(
0
.
71
,
0
)(
0
.
71
,
0
.
08
)(
0
.
71
,
0
.
08
)
(
1
,
0
)
(
0
.
71
,
0
.
08
)
(
0
.
71
,
0
.
08
)(
0
.
71
,
0
)(
0
.
71
,
0
.
08
)(
0
.
71
,
0
.
08
)
(
1
,
0
)
Therefore,
Z
2
is an intuitionistic fuzzy equivalence matrix.
Step 3
By Eq. (
2.33
), we can see that the value of confidence level
λ
is only related
to the membership degree
μ
z
ij
and the non-membership degree
v
z
ij
of the elements
z
ij
=
(μ
z
ij
,
in the intuitionistic fuzzy equivalence matrix
Z
∗
=
Z
2
z
ij
)
5
×
5
.In
v
z
ij
)
=
(
general, we can make a detailed discussion by taking
v
z
ij
corresponding
to each element of
Z
∗
as the bounded values of the confidence level
μ
z
ij
and 1
−
λ
of the
λ
-cutting
matrix
λ
Z
∗
:
(1) When
λ
≤
0
.
71, we have
⎛
⎝
⎞
⎠
11111
11111
11111
11111
11111
Z
∗
=
λ
(2) When 0
.
71
<λ
≤
0
.
78, we have
⎛
⎞
111
1
2
1
2
⎝
⎠
111
1
2
1
2
111
1
2
1
2
Z
∗
=
λ
1
2
1
2
1
2
1
2
1
1
2
1
2
1
2
1
2
1
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