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()
α =
3. Definition of a precise value of a conclusion variable
μ
z
.
2
2
C
2
α
z
+
α
z
z
=
1
1
2
2
.
0
α
+
α
Example 1.11.
Application of Tsukamoto algorithm. As in the example 1.10, let
us assume that ranges of values of variables
X
,
Y
,
Z
are segments [2.10], [1.5],
[3.8], accordingly. Linguistic values of variables (
X
—
1
2
~
~
~
~
,
Y
—
,
B
,
B
A
,
A
1
2
1
2
~
~
Z
—
) have the membership functions shown in Fig. 1.11.
C
,
C
1
2
()
()
()
μ
5
=
0
25
μ
5
=
0
75
μ
4
=
0
Let
x
=
5
;
y
=
4
, then
;
;
;
~
~
~
A
0
0
A
B
2
1
1
()
μ
4
=
0
~
.
B
2
[
]
() ()
(
)
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
0
A
B
2
2
z
,
z
from the equations:
Let us find
z
−
3
0
=
μ
=
1
−
1
;
~
1
C
5
z
−
8
0
25
=
μ
=
1
+
2
.
~
C
5
2
Then
;
z
=
4
25
, and the defuzzification gives:
z
=
3
1
2
3
⋅
0
+
4
25
⋅
0
25
z
=
=
4
036
.
0
0
+
0
25
