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In-Depth Information
=
=
Example 2.3.2
A linguistic variable has the fuzzy values
H
high
,
S
short
and
=
M
medium
, with
H
represented by
⊧
⊨
0
,
if 0
x
5
μ
H
(
x
)
=
1
,
if 7
x
10
⊩
x
−
5
,
if 5
x
7
.
2
H
S
, and that
M
is the aggregation of
H
and
S
In the two suppositions,
M
=
·
under the weighted mean
A
(
x
1
,
x
2
)
=
0
.
3
x
1
+
0
.
7
x
2
, compute
μ
M
.
μ
H
is monotonic,
μ
S
(
)
=
μ
H
(
−
)
Solution.
Since
S
is an antonym of
H
, and
x
10
x
,
that is
⊧
⊨
1
,
if 0
x
3
μ
S
(
x
)
=
0
,
if 5
x
10
⊩
5
−
x
,
.
if 3
x
5
2
The solution for the first supposition appears in the following sequence of figures
(with
,
=
·=
min
1
−
id).
The solution for the second supposition is
⊧
⊨
0
.
7
,
if 0
x
3
0
.
7
(
5
−
x
)
,
if 3
x
5
2
μ
H
(
x
)
=
μ
A
(
H
,
S
)
(
x
)
=
0
.
3
(
x
−
5
)
⊩
,
if 5
x
7
2
0
.
3
,
if 7
x
10
,
graphically,
0.7
M
0.3
3
5
7
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