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In-Depth Information
•
∈[
,
]
(
,
)
(
,
)
For
t
6
8
,
R
is the segment joining
6
1
and
8
0
, that is
xy
1
611
801
8
−
x
0
=
=
x
+
2
y
−
8
,
or
y
=
2
Graphically
Notice that the result is also a fuzzy number
μ
6
, such that the amplitude of it
(
. When
operating with fuzzy numbers, the amplitude grows. If there is uncertainty about the
value 3, the uncertainty about 3
[
8
,
4
]
,
8
−
4
=
4) is twice than that of the initial
μ
3
(
[
2
,
4
]
,
4
−
2
=
2
)
+
3 is twice, and such uncertainty will grow each
time we 'add' more numbers.
6.2.2 Operations with Triangular Fuzzy Numbers
Let's show a systematic way of operating with triangular fuzzy numbers, that is,
those represented by
⊧
⊨
L
(
x
),
if
x
∈
(
a
,
n
)
μ
n
(
x
)
=
R
(
x
),
if
x
∈
(
n
,
b
)
⊩
0
,
otherwise
,
with
L
and
R
linear functions, and
μ
n
(
n
)
=
1. Graphically,
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