Image Processing Reference
In-Depth Information
Therefore, in general for any positive integer
n
,
n
n
n
Ax x
=
{,[()] ,
μ
11
− −
(
ν
())}
x
A
A
and follows the condition
n
n
0
≤
[()] [( ())]
μ
x
+ −− ≤
1
1
ν
x
1
A
A
Like fuzzy sets, for IFSs, linguistic hedges can be defined:
CON(
A
) = very (
A
)
DIL(
A
) = more or less
A
plus(
A
) =
A
1.25
minus(
A
) =
A
0.75
Example 1.1
Let
A
be an IFS denoting the linguistic variable 'YOUNG' in the universe
of discourse [0, 100]:
A
(
YOUNG
)
=
{( ,
x
μ
( ),
x
ν
())|
x xU
∈
}
YOUNG(
A
)
YOUNG()
A
where
μ
YOUNG
()
x
=
1
,
x
∈
⎣
0 28
,
⎦
1
=
,
x
∈
⎣
28 100
,
⎦
(
)
(
285
2
)
1
(
)
/
+−
x
ν
YOUNG
()
x
=
0
,
x
∈
0 30
,
⎣
⎦
1
=−
1
,
x
∈
⎣
30 100
,
⎦
(
)
(
305
2
)
1
+−
(
x
)
/
'VERY YOUNG' may be denoted as
VERY YOUNG
=
{( ,
x
μ
( ),
x
ν
())|
xxU
∈
}
VERY YOUNG
VERYYOUNG
where
μ
() ,
x
=
1
x
∈
⎣
0 28
,
⎦
VERY YOUNG
1
=
,
x
∈
⎣
28 100
,
⎦
(
)
2
2
1
+
(( ))
x
−
285
/
Search WWH ::
Custom Search