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-cutting matrix
C
λ
=
λ
c
ij
6
×
6
of
C
is:
λ
=
.
λ
(6) If
0
977, then the
⎛
⎞
100001
011111
011111
011111
011111
111111
⎝
⎠
C
λ
=
Similar to (4),
y
i
(
=
,
,...,
)
i
1
2
6
are grouped into the following one types:
{
y
1
,
y
2
,
y
3
,
y
4
,
y
5
,
y
6
}
2.8 A Netting Method for Clustering Intuitionistic
Fuzzy Information
2.8.1 An Approach to Constructing Intuitionistic Fuzzy
Similarity Matrix
Now we consider a multi-attribute decision making problem, let
Y
and
G
be as
defined previously. The characteristic of each alternative
y
i
under all the attributes
G
j
(
j
=
1
,
2
,...,
n
)
is represented as an IFS:
y
i
={
G
j
,μ
y
i
(
G
j
),
v
y
i
(
G
j
)
|
G
j
∈
G
}
,
i
=
1
,
2
,...,
m
;
j
=
1
,
2
,...,
n
(2.185)
where
μ
y
i
(
G
j
)
denotes the membership degree of
y
i
to
G
j
, and
v
y
i
(
G
j
)
denotes the
non-membership degree of
y
i
to
G
j
. Obviously,
π
y
i
(
G
j
)
=
1
−
μ
y
i
(
G
j
)
−
v
y
i
(
G
j
)
is the uncertainty (or hesitation) degree of
y
i
to
G
j
.Iflet
r
ij
=
(μ
ij
,
v
ij
)
=
(μ
y
i
(
G
j
),
v
y
i
(
G
j
))
(
=
,
,...,
;
, which is an IFV, then based on these IFVs
r
ij
i
1
2
m
r
ij
)
m
×
n
.
Next, we shall introduce an approach to constructing an intuitionistic fuzzy sim-
ilarity matrix based on the intuitionistic fuzzy matrix
R
=
,
,...,
)
×
=
(
j
1
2
n
, we can construct an
m
n
intuitionistic fuzzy matrix
R
r
ij
)
m
×
n
.
For any two alternatives
y
i
and
y
k
, we first use the normalized Hamming distance
to get the average value of the absolute deviations of the non-membership degrees
v
ij
and
v
kj
, for all
j
=
(
=
1
,
2
,...,
n
:
n
1
n
d
NH
(
y
i
,
y
k
)
=
1
|
v
ij
−
v
kj
|
,
i
,
k
=
1
,
2
,...,
m
(2.186)
j
=
Analogously, we get the average value of the absolute deviations of the member-
ship degrees
μ
ij
and
μ
kj
, for all
j
=
1
,
2
,...,
n
:
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