Page 130 - Control Theory in Biomedical Engineering

116 Control theory in biomedical engineering

N
X
E i
i¼1
μ ¼ (7)
N

v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
N
u
X
u 2
ð E i μÞ
u
t
i¼1
δ ¼ (8)
N
where, N refers to the number of feature vectors to be classified.
The fuzzy sets are illustrated in Fig. 11. Therefore it is clear that for each
input there is a coverage rate between its fuzzy set compared to its discourse
universe.
• Operator adjustment
Fuzzy logic if-then rules are formed by applying fuzzy operations to the
fuzzy sets. Fuzzy operators are used to compute the rules weight. They
include the intersection (AND), the union (OU), the fuzzy implication
and the Cartesian product. It is recommended to adjust them carefully.
Table 2 shows the selected operators. The product and the sum of the
fuzzy sets are associated with the conjunction "AND" and the disjunction
"OR," respectively. The product method is used for the fuzzy implication.
It is used to adjust the consequence membership function based on the ante-
cedent values.
• Rule base construction
After achieving the input/output identification, the partition of the various
discourse universes, the inference fuzzy mechanism selection and the fuzzy
operators adjustment, it is possible to define the rule base. It imitates the rela-
tionship between the fuzzy sets and the five classes. Therefore, by referring
to the cardiologist’s knowledge, five rules haves been developed. Table 3
shows the comportment of the six features to identify the five arrhythmia
classes.
Table 3 leads us to create the rule base, which is described linguistically in
Table 4.
The fuzzy rules, described in Table 4, have the form of conditional
expression linking the states of the input features as antecedent and the five
outputs as consequences. It can be represented in another form, as it is
described in Table 5.