WARP11 Datasheet, PDF (8/19 Pages) STMicroelectronics – WEIGHT ASSOCIATIVE RULE PROCESSOR

W.A.R.P.1.1
Figure 6. Inference Unit Structure
by the configuration in accordance with the antece-
dent part of the fuzzy rules. The duration of the
fuzzification process depends from the chosen
configuration and the input number.
Inference Unit. Thanks to the Theta Operator, the
Inference Unit generates the THETA weights which
are used to manipulate the consequent MFs.
This is a calculation of the maximum and/or mini-
mum performed on ALPHA values according to the
logical connectives of fuzzy rules. It is possible to
utilize the AND/OR connectives and to directly ex-
ploit ALPHA weights or the negated values. The
number of THETA weights depends on the number
of rules.
The rules can have at maximum four ALPHA
weights (however they are connected). Two or
more rules can be only joined with the OR connec-
tive.
Inference Unit structure is shown in figure 5.
Defuzzifier. It generates the output crisp values
implementing the consequent part of the rules ac-
cording to MAX-DOT method.
In this method consequent MFs are multiplied by a
weight value Ω (OMEGA), which is calculated on
the basis of antecedent MFs and logical operators.
All the terms needed to evaluate sums in numerator
and denominator of center of gravity equation (see
formula) are stored during the off-line phase.
The processing of fuzzy rules produces, for each
output variable, a resulting membership function.
Each MF related to the processed output variable
is firstly modified by a rule weight in accordance to
MAX-DOT method.
Output value (X) is deduced from the centroids (xi)
and the modified MFs (Ωi *Ai) by using the formula:
n
∑ ^{Ωi ∗ Ai ∗ xi}
X= ¹ _n
∑ ^Ωi ^{∗ A}i
1
n = number of MFs defined for the Output Variable
A_i= MF_i Area
x_i=absciss of the MF_i centroid
Ωi =membership degree of the output MFi.
To represent a membership function related with
the THEN-part of a rule W.A.R.P. uses a single
memory bench. For each consequent MF each
memory word contains both the area multiplied with
the barycentre and the area itself. This area is
related to the first truth level (there are 16 truth
levels (4 bit), so a multiplication with the calculated
THETA must be performed on-line.
Two parallel blocks calculate the numerator and
denominator values to implement the centroids
formula. A final division block calculates the output
values (see figure 6).
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