Image Processing Reference
In-Depth Information
The hesitation degree also lies in an interval which is given as
⎣
−
+
⎦
=− −
⎣
−
−
+
+
⎦
ππ μ
(), ()
x
x
1
( )
x
ν
( ),
x
1
−
μ
() ()
x
−
ν
x
A
A
A
A
A
A
If
μ
() (),
then IVIFS becomes IFS.
For two interval-valued fuzzy sets,
() ()
and
ν
−
x
=
μ
+
x
−
x
=
ν
+
x
A
A
A
A
{
}
IVIFS
⎣
−
+
⎦
⎣
−
+
⎦
A
=
x
,
μμ ν
( ), (),
x
x
( ), ()
x
ν
x xX
∈
A
A
A
A
and
{
}
IVIFS
⎣
−
+
⎦
⎣
−
+
⎦
B
=
x
,
μμ νν
( ), (),
x
x
( ), ()
x
x xX
∈
B
B
B
B
the following relation holds:
1.
AB x
⊆
,
iff
μ
−
( )
≤
μ
−
( ), () (), ()
x
μ
+
x
≤
μ
+
x
ν
−
x
≥
ν
−
( ), ()
x
ν
+
x
≥
ν
+
()†
x
A
B
A
B
A
B
A
B
for
xX
∈
2.
A
=
B
, iff
A
⊆
B
and
B
⊆
A
3.
Ax
c
IVIFS
=
{,[(),
ν
−
x
ν μμ
+
( )],[(), ()]|
x
−
x
+
x xX
∈
}
A
A
A
A
4.
AB
∩=
[min((),
μμ μμ
−
x
−
( )),min( (), ())],
x
+
x
+
x
A
B
A
B
[max((),
ν
−
x
ν
−
( )),max( (), ())]
x
ν
+
x
ν
+
x
A
B
A
B
5.
AB
∪=
[max((),
μμ μμ
−
x
−
( )),max( (), ())],
x
+
x
+
x
A
B
A
B
−
ν
−
+ +
( )),min( (), ())]
[min((),
ν
x
x
ν
x
ν
x
A
B
A
B
6.
AB x
+= +
[( () () () ( )),(()
μ
−
μ μμμ
−
x
−
−
x
⋅
−
x
+
x
+
μ μ
B
+
( )
x
−
+
( )
x
⋅
+
( ))]
x
A
B
A
B
A
B
A
−
−
+
+
[()
ν
x
⋅
ν
( ), () ()]
x
ν
x
⋅
ν
x
A
B
A
B
λ
−
λ
+
λ
−
λ
+
λ
7.
A
=
[
μ
( ), (),
x
μ
x
11
− −
(
ν
()), (
x
11
− −
ν
( )) ]
x
A
A
A
A
8.
AB
⋅= ⋅
[()
μμμμ
−
x
−
( ), () ( )],
x
+
x
⋅
+
x
A
B
A
B
−
−
−
ν
−
+
+
+
+
[()
ν
x
+
ν
( )
x
−
ν
( )
x
⋅
(), ()
x
ν
x
+
ν
( )
x
−
ν
( )
x
⋅
ν
( )]
x
A
B
A
B
A
B
A
B
Correlation coefficient using interval valued intuitionistic fuzzy sets (IVIFS)
is studied by authors [6,13]. For two IVIFS
A
and
B
, if
1
2
μμμμν
∑
⎣
−
−
+
+
−
−
+
+
⎦
CAB
(,)
=
( )
x
⋅
( )
x
+
( )
x
⋅
( )
x
+
( )
x
⋅
ν
( )
x
+
ν
( )
x
⋅
ν
B
x
()
, then
A
B
A
B
A
B
A
CAB
CAACBB
(,)
(,)( )
Corr(,)
AB
=
⋅
⋅
Search WWH ::
Custom Search