Page 129 - Control Theory in Biomedical Engineering

Genetic fuzzy logic based system for arrhythmia classification 115

describes the defuzzification of the output variables, which converts the
fuzzy outputs into crisp ones (Zadeh, 2015).
Generally, the fuzzy arrhythmia classifier has to undergo some adjust-
ment in the knowledge base in terms of number of fuzzy variables, the mem-
bership functions types and the definition of rules. We have considered the
following steps in order to configure the proposed FLC.
• Inference mechanism
We have selected the Mamdani fuzzy inference mechanism whose outputs
are defined as singletons. In fact, the used defuzzification function is based on
the weight of the most important fuzzy rule.
• Input/output identification
The morphological features, previously extracted in during pre-processing,
are considered as the FLC inputs. Indeed, we have chosen six of them,
including the mean heart rate (E1), the P wave amplitude (E2), the PR inter-
val duration (E3), the QRS complex duration (E4), the RR interval dura-
tion (E5) and the ST interval duration (E6). In addition, for the FLC outputs,
we have five arrhythmia classes (NSR, PVC, P, LBBB and RBBB).
• Discourse universe partition
We have considered for each input (E i ) three fuzzy sets as follows: the min-
imum (MIN), medium (MOY) and maximum (MAX). These fuzzy sets are
defined on the six discourse universes [ E i +E i ]. The Gaussian membership
functions are used for the inputs. However, the output membership func-
tions are singletons.
In order to define the fuzzy sets, the mean value (μ) and the standard
deviation (δ) are determined for each input. They are defined in Eqs. (7)
and (8), respectively. The lower limit (μ 2*δ), the average (μ) and the
upper limit (μ+2*δ), are used to deduce the fuzzy sets (MIN, MOY and
MAX) for the six inputs E i (with (i¼1 … 6)). They are represented in
Table 1.

Table 1 Fuzzy sets.
Input Fuzzy sets
MIN E i <μ 2 * δ
E i
MOY μ 2 * δ < E i < μ+2 * δ
MAX E i > μ+2 * δ