Information Technology Reference
In-Depth Information
∀
∈
(0,1]
, A
ȹ
is a
(1) A is called closed convex fuzzy set on R if and only if
closed convex set, that is to say, A
ȹ
is a closed interval.
(2) A is called regular fuzzy set on R if and only if ∃x0∈R then A(x0)=1x0 is
called regular point of A
(3) If
∀
∈
(0,1]
, and A
ȹ
is a set with boundary, A is called fuzzy set with
boundary.
(4) A regular convex fuzzy set on R is called a fuzzy number, a regular closed
convex fuzzy set is called a closed fuzzy number and a regular closed convex
fuzzy set with boundary is called a closed fuzzy number with boundary.
θ
!
is a
1,
x
x
=
0
Ê
=
Ë
!
θ
zero fuzzy number and
0,
≠
0
Ì
(5) Suppose A is a fuzzy number, if all numbers in supp A=x
∈
RA(x)0
is positive real number, then A is called positive fuzzy number. All the positive
fuzzy number with boundary is marked as G,
!
G
.
G
=
G
{ }
θ
~
~
“
≤
” in
G
∀
A
,
B
∈
G
A
≤
B
Definition 12.4
is defined as:
,
if and only if
λ
λ
λ
λ
λ
λ
λ
λ
∀λ
∈
(
0
a
≤
b
a
≤
b
A
=
[
a
,
a
]
B
=
[
b
,
b
]
for
,
and
.
,
.
1
1
2
2
λ
1
2
λ
1
2
~
“
≤
” is partial order in
G
.
~
A
,
B
∈
G
Definition 12.5
Suppose
, then:
(
A
+
B
)( )
z
=
∨
(
A x
( ))
∧
B y
(
)),
∀ ∈
z
R
x
+
y
=
z
(
A
−
B
)( )
z
=
∨
(
A x
( ))
∧
B y
(
)),
∀ ∈
z
R
x
−
y
=
z
(
A
×
B
)( )
z
=
∨
(
A x
( ))
∧
B y
(
)),
∀ ∈
z
R
x
+
y
=
z
