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≤
·
=
≤
≤
(μ
3
μ
3
)(
)
=
1. If
t
4, and
x
y
t
, either
x
2, or
y
2. Hence,
t
0.
≥
,(μ
3
μ
3
)(
)
=
Analogously, if
t
16
t
0.
Obviously,
(μ
3
μ
3
)(
9
)
=
1.
2. Hence,
L
will be defined in
[
4
,
9
]
, and
R
in
[
9
,
16
]
.
3. If
x
,
y
∈[
2
,
3
]
,itis
x
·
y
∈[
4
,
9
]
, hence,
L
(
t
)
=
Sup
t
=
x
·
y
min
(
x
−
2
,
y
−
2
)
=
ʱ
⃒
ʱ
=
x
−
2
, ʱ
=
y
−
2
⃒
ʱ
=
√
t
2
⃒
x
=
ʱ
+
2
,
y
=
ʱ
+
2
⃒
t
=
x
·
y
=
(ʱ
+
2
)
−
2
.
4. If
x
,
y
∈[
3
,
4
]
,itis
x
·
y
∈[
9
,
16
]
, hence,
R
(
t
)
=
Sup
t
min
(
4
−
x
,
4
−
y
)
=
ʱ
⃒
ʱ
=
4
−
x
, ʱ
=
4
−
y
=
x
·
y
−
√
t
2
⃒
x
=
4
−
ʱ,
y
=
4
−
ʱ
⃒
t
=
(
4
−
ʱ)
⃒
ʱ
=
4
.
Finally,
⊧
⊨
⊫
⊬
⊭
=
μ
9
(
√
t
−
2
,
if
t
∈[
4
,
9
]
−
√
t
(μ
3
μ
3
)(
t
)
=
4
,
if
t
∈[
9
,
16
]
t
).
⊩
0
,
otherwise
.
Graphically
Remark 6.2.2
It should be pointed out that, in the case of the product of triangular
fuzzy numbers, the result is not a triangular (linear) fuzzy number, since functions
L
and
R
are not linear. In addition the interval
[
a
,
b
]
is not symmetrical. Look that for
μ
9
is
[
4
,
16
]
whose mid point is not 9 but 10.
Let's now consider the quotient
÷
of fuzzy numbers defined by
(μ
n
÷
μ
m
)(
t
)
=
Sup
t
min
(μ
n
(
x
), μ
m
(
y
)),
x
y
=
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