Information Technology Reference
In-Depth Information
l
l
l
n
n
l
1
,
α
1
,β
1
...
l
n
,
α
,β
k
k
O
3
α
O
3
α
k
1
,
α
1
,β
1
3
(
μ
k
1
,
l
1
,ν
k
1
,
l
1
). . .
3
(
μ
k
1
,
l
n
,ν
k
1
,
l
n
)
,β
,β
3
3
=
.
.
.
.
. . .
m
,β
m
O
3
α
O
3
α
k
m
,
α
3
(
μ
k
m
,
l
1
,ν
k
m
,
l
1
)...
3
(
μ
k
m
,
l
n
,ν
k
m
,
l
n
)
,β
,β
3
3
In the second case, the form of the triple of operators is
O
1
O
2
O
3
(
α
1
,β
1
,
α
2
,β
2
,
α
3
,β
3
)(
A
)
O
2
α
l
l
O
2
α
l
n
,β
n
)
l
1
,
2
(
α
1
,β
1
)...
l
n
,
2
(
α
,β
,β
2
2
O
1
α
k
k
O
3
α
O
3
α
k
1
,
(
α
1
,β
1
)
(
μ
k
1
,
l
1
,ν
k
1
,
l
1
) ...
(
μ
k
1
,
l
n
,ν
k
1
,
l
n
)
,β
,β
,β
1
1
3
3
3
3
.
.
.
.
...
=
.
O
1
α
k
k
O
3
α
O
3
α
k
i
,
(
α
i
,β
i
)
(
μ
k
i
,
l
1
,ν
k
i
,
l
1
)...
(
μ
k
i
,
l
n
,ν
k
i
,
l
n
)
,β
,β
,β
1
1
3
3
3
3
.
.
.
.
...
O
1
α
m
,β
m
)
O
3
α
O
3
α
k
m
,
1
(
α
3
(
μ
k
m
,
l
1
,ν
k
m
,
l
1
)
...
3
(
μ
k
m
,
l
n
,ν
k
m
,
l
n
)
,β
,β
,β
1
3
3
2.8 An Example with Intuitionistic Fuzzy Graphs
Let
V
={
v
1
,v
2
,...,v
n
}
be a fixed set of vertices and let each vertex
x
have a degree
of existence
α(
x
)
and a degree of non-existence
β(
x
)
. Therefore, we can construct
the IFS
V
∗
={
x
,α(
x
), β(
x
)
|
x
∈
V
}={
v
i
,α(v
i
), β(v
i
)
|
1
≤
i
≤
n
}
,
where for each
x
∈
V
:
α(
), β(
), α(
)
+
β(
)
∈[
,
]
.
x
x
x
x
0
1
Let
H
be a set of arcs between vertices from
V
. We again can juxtapose to each
arc a degree of existence
μ(
x
,
y
)
and a degree of non-existence
ν(
x
,
y
)
. Therefore,
we can construct the new IFS
H
∗
={
x
,
y
,μ(
x
,
y
), ν(
x
,
y
)
|
x
,
y
∈
V
}
={
v
i
,v
j
,μ(v
i
,v
j
), ν(v
i
,v
j
)
|
1
≤
i
,
j
≤
n
}
,
where for each
x
,
y
∈
V
:
μ(
x
,
y
), ν(
x
,
y
), μ(
x
,
y
)
+
ν(
x
,
y
)
∈[
0
,
1
]
.
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