Supported format of rules – Rockwell Automation RSLogix 5000 Fuzzy Designer User Manual
Page 48
Publication LOGIX-UM004A-EN-P - March 2007
48 FuzzyDesigner Component Library
Supported Format of Rules
Multiple notations are used in the explanation of the supported format
of rules.
• X
1
, X
2
,…, X
n
– premise variables
• Y
1
, Y
2
,…, Y
m
. – consequent variables
• A
i1
, A
i2
,… – terms defined for the premise variable X
i
• B
j1
, B
j2
,… – terms defined for the consequent variable Y
j
FuzzyDesigner also supports the OR operator.
The rule block component performs fuzzy logic inference based on
fuzzy rules. In a simplified way, it computes degrees of fulfillment of
consequent variables from degrees of fulfillment of premise variables
by using fuzzy t-norms and s-norms (t-conorms).
FuzzyDesigner supports the following t-norms (fuzzy AND operators):
• Minimum: T
min
(x, y) = min (x, y)
• Product: T
prod
(x, y) = x
·
y
EXAMPLE
IF (X
1
IS A
13)
AND (X
2
IS A
21
) AND … AND (X
n
IS A
n1
) THEN
(Y
1
IS B
12
) [w
1
] , (Y
2
IS B
21
) [w
2
], … (Y
n
IS B
n3)
[w
n
]
where w
k
∈ [0,1] is rule weight of the k-th consequent.
Schematically the rule can be rewritten as follows:
(A
13
, A
21
, … , A
n1
)
Æ
(B
12
[w
1
] , B
21
[w
2
] , … , B
n3
[w
n
] )
This rule base format is very useful in manual design. It can be
represented in the form of a table where every column
corresponds to one variable and rows of the table are filled
with appropriate terms or optionally with their inversions
(applying the NOT operator).
EXAMPLE
IF [(X
1
IS A
11
) OR (X
1
IS A
12
) OR ... ] AND (X
2
IS A
21
) AND …
AND (X
n
IS A
n1
) THEN (Y
1
IS B
12
)
You define the number of terms in the OR expression.
The NOT operator can be applied to the whole OR expression.
IF [ NOT [(X
1
IS A
11
) OR (X
1
IS A
12
) OR ... ]] AND (X
2
IS A
21
)
AND … AND (X
n
IS A
n1
) THEN (Y
1
IS B
12
) [w
1
] , (Y
2
IS B
21
)
[w
2
], …