Information Technology Reference
In-Depth Information
Sugeno Algorithm
For this algorithm the following conclusion rules are used:
A
and
y
is
B
then
z
=
a
x
+
b
y
if
X
is
;
1
1
1
1
A
and
y
is
B
then
z
=
a
x
+
b
y
if
X
is
.
2
2
2
2
1.
Fuzzification is the same as in Mamdani algorithm.
2.
A fuzzy conclusion is the same as in Mamdani algorithm.
[
]
()
()
α
=
min
μ
x
,
μ
y
;
~
1
0
B
0
A
1
1
[
]
()
()
α
=
min
μ
x
,
μ
y
.
~
~
2
0
0
A
B
2
2
Individual outputs of the rules:
z
=
a
x
+
b
y
;
1
1
0
1
0
z
=
a
x
+
b
y
.
3.
Definition of precise value of a conclusion variable (the same as in
Tsukamoto algorithm)
2
2
0
2
0
α
z
+
α
z
z
=
1
1
2
2
.
0
α
+
α
1
2
Larsen Algorithm
1.
Fuzzification is the same as in Mamdani algorithm.
2.
Fuzzy conclusion is 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
Definition of particular fuzzy sets:
()
μ
=
α
μ
z
;
~
1
1
C
C
()
1
μ =
3.
Composition. Union of truncated membership functions (the same as in
Mamdani algorithm)
α
μ
z
.
~
2
2
C
C
2
[
]
()
()
()
μ =
Σ
4.
Defuzzification (the same as in Mamdani algorithm):
for a continuous case
z
max
μ
z
,
μ
z
.
~
~
1
1
1
2
C
C
