Image Processing Reference
In-Depth Information
ν
() ,
x
=
0
x
∈
⎣
0 30
,
⎦
VERY YOUNG
1
=
1
−
,
x
∈
⎣
30 100
,
⎤
⎦
(
)
2
1
+
(( ))
x
−
305
/
2
Likewise, 'MORE OR LESS YOUNG' may be defined as
μ
() ,
x
=
0
x
∈
⎣
0 28
,
⎦
MOREOR LESSYOUNG
1
=
,
x
∈
⎣
28
,
100
⎦
(
2
12
)
/
1
+
(( ))
x
−
285
/
() ,
1
0 30
,
ν
x
=
x
∈
⎣
⎦
MOREOR LESSYOUNG
1
=
1
−
,
x
∈
⎣
3
0 100
,
⎦
(
2
12
)
/
1
+
(( ))
x
−
305
/
1.4 Fuzzy Complement and Intuitionistic Fuzzy Generator
Fuzzy complement is used in creating IFSs. Fuzzy complement is a fuzzy
negation. Suppose
μ(
x
) is defined as the degree to which
x
belongs to
A
. Let
c
· μ(
x
) denote a fuzzy complement of
A
that signifies the degree to which
x
belongs to the fuzzy complement set
cA
. Then the complement
cA
is defined
by a function
c
: [0, 1] → [0, 1].
The fuzzy complement operator has the following properties:
Boundary condition
c
()
0
=
1and
c
()
1
=
0
Involutive property
cc x
⋅
μ
=
μ
x
(()) ()
Monotonicity
For all
a
,
b
∈ [0, 1], if
a
≤
b
, then
c
(
a
) ≥
c
(
b
)
c ·
μ(
x
) is continuous
The fuzzy complement function has been studied by many authors [8,15,17].
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