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Fig. 1.9
Membership functions of variables according to Mamdani algorithm:
(
)
~
~
~
~
~
~
(
)
(
)
a —
; b —
; c —
Y
B
,
B
X
A
,
A
Z
C
,
C
1
2
1
2
1
2
Example 1.10.
Application of Mamdani algorithm. Let us assume that ranges of
values of variables
X
,
Y
,
Z
are segments [2; 10], [1; 5], [3; 8], accordingly.
Linguistic values of these variables (
X
—
~
C
~
~
~
~
~
,
Y
—
,
Z
—
) have
B
,
B
C
A
,
A
1
2
1
2
1
2
the membership functions shown in Fig. 1.9.
()
()
()
y
=
4
μ
5
=
0
75
μ
5
=
0
25
μ
4
=
0
Let
;
, then
;
;
;
x
=
5
~
~
~
0
A
A
B
0
1
2
1
()
μ
4
=
0
.
~
B
2
Then
