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[
]
()
()
(
)
α
=
min
μ
x
,
μ
y
=
min
0
75
;
0
,
=
0
~
~
1
0
0
A
B
1
1
[
]
()
()
(
)
α
=
min
μ
x
,
μ
y
=
min
0
25
;
0
=
0
25
.
~
~
2
0
B
0
A
2
2
The composition of the truncated membership functions is presented in Fig. 1.10.
As a result we'll obtain:
4
,
2
4
,
5
8
(
)
∫
∫
∫
0
xdx
+
0
x
−
2
xdx
+
0
25
xdx
z
=
∫
3
4
,
2
4
,
5
=
0
4
,
2
4
,
5
8
(
)
∫
∫
0
dx
+
0
x
−
2
dx
+
0
25
dx
3
4
,
2
4
,
5
(
)
(
) (
)
0
05
4
2
2
−
3
2
+
0
167
4
3
−
4
2
3
−
4
2
−
4
2
2
+
=
→
(
)
(
)
(
)
2
2
0
4
2
−
3
+
0
25
4
−
4
2
−
2
4
−
4
2
+
(
)
2
2
+
0
125
8
−
4
→
=
5
86
.
(
)
+
0
25
8
−
4
Fig. 1.10
A composition of the truncated membership functions
Algorithm of Tsukamoto
It is assumed that membership functions
()
()
μ
z
μ
z
,
are monotone.
C
~
C
~
1.
Fuzzification. The same as in Mamdani algorithm.
2.
Fuzzy conclusion (the same as in Mamdani algorithm)
[
]
()
()
α =
min
μ
x
,
μ
y
;
~
~
1
0
0
A
B
1
1
[
]
()
()
α
=
min
μ
x
,
μ
y
.
~
~
2
0
0
A
B
2
2
z
,
z
are derived from the equations
()
Precise values
α
=
μ
z
;
~
1
1
C
1
