
bythe configurationinaccordancewith theantece-
dent part of the fuzzy rules. The duration of the
fuzzification process depends from the chosen
configurationand the inputnumber.
InferenceUnit
. Thanksto the ThetaOperator, the
InferenceUnitgeneratesthe THETAweights which
areused to manipulatethe consequentMFs.
This is a calculation of the maximum and/or mini-
mum performedon ALPHAvalues accordingto the
logical connectives of fuzzy rules. It is possible to
utilize the AND/OR connectives and to directlyex-
ploit ALPHA weights or the negated values. The
numberof THETAweightsdepends onthe number
ofrules.
The rules can have at maximum four ALPHA
weights (however they are connected). Two or
more rules canbe only joinedwith theOR connec-
tive.
InferenceUnit structure is shown in figure 5.
Defuzzifier
. It generates the output crisp values
implementing the consequentpart of the rules ac-
cording to MAX-DOT method.
In this method consequentMFs are multiplied by a
weight value
(OMEGA
)
, which is calculated on
the basis of antecedentMFs and logical operators.
Allthetermsneededtoevaluatesumsinnumerator
and denominatorof 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 firstlymodified by a rule weight in accordanceto
MAX-DOT method.
Output value(X) is deduced fromthe centroids (x
i
)
and themodified MFs (
i
*A
i
) by usingthe formula:
X
=
∑
1
n
i
A
i
x
i
∑
1
n
i
A
i
n = numberof MFsdefinedforthe Output Variable
A
i
= MF
i
Area
x
i
=absciss of the MF
i
centroid
i
=membershipdegree of the output MF
i
.
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
memorywordcontainsboththeareamultipliedwith
the barycentre and the area itself. This area is
related to the first truth level (there are 16 truth
levels (4bit), so amultiplication with the calculated
THETAmust be performed on-line.
Two parallel blocks calculate the numerator and
denominator values to implement the centroids
formula. Afinal division blockcalculates theoutput
values (see figure 6).
Figure6. InferenceUnit Structure
8/19
W.A.R.P.1.1