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μ
3
with
ʱ
=
μ
8
with
ʲ
=
μ
3
↕
μ
8
=
μ
11
with
For example,
1, and
2, give
ʱ
+
ʲ
=
3, that is the triangle on
[
11
−
3
,
11
+
3
]=[
8
,
14
]
.
Let's take into account the substraction
μ
n
μ
m
=
μ
n
[
(
−
1
)
μ
m
]
, with
)
=
μ
m
t
1
((
−
1
)
μ
m
)(
t
=
μ
m
(
−
t
)
, that means
−
with
−
μ
m
=
(
−
1
)
μ
m
. The fuzzy number
−
μ
m
is obtained by translating
μ
m
symmetrically at the other side of
x
=
0. For example, with
⊧
⊨
x
−
2
,
if
x
∈
(
2
,
3
)
μ
3
(
x
)
=
4
−
x
,
if
x
∈
(
3
,
4
)
⊩
0
,
otherwise
,
it results
⊧
⊨
⊫
⊬
t
+
2
,
if
x
∈
(
−
2
,
0
)
2
2
−
t
(μ
3
μ
3
)(
t
)
=
,
∈
(
,
)
if
x
0
2
⊩
2
⊭
0
,
otherwise
.
=
μ
0
(
t
),
with the interval
[
a
,
b
]=[−
2
,
+
2
]
.
μ
n
μ
m
of two triangular fuzzy numbers, the
method is the same of the sum, but remembering that since
For what concerns the product
(μ
n
μ
m
)(
t
)
=
Sup
t
=
x
·
y
min
(μ
n
(
s
), μ
m
(
y
))
,thevalue
t
will be reached by the product
x
·
y
. For example,
with
μ
3
as below, let's compute
μ
3
μ
3
. The process is as follows.
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