Biomedical Engineering Reference
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NDE
Fig. 3.13
Membership function of
NDE
The above reasons explained why vague words were used instead of precise numer-
ical value. Now we explain how to process the vague definition. To evaluate the vague
quantities to come up with a decision is not a trivial challenge. This process is designed
in fuzzy system framework, which is a well-known logic framework in processing
these interconnected multistage vague decisions in Fig.
3.12
in order to produce a
desired response to establish the automated control on the quadruple division scheme.
The formulation of
NDE
,
NCL
, HDT, and
CER
defined in Eqs. (
3.54
), (
3.55
),
(
3.56
) and (
3.57
), respectively, can be perceived as inputs in establishing fuzzy
membership functions in fuzzy logic controller using intuitive approach. Each
fuzzy membership of Eqs. (
3.54
), (
3.55
), (
3.56
) and (
3.57
) is illustrated graphi-
cally as follow in Figs.
3.13
,
3.14
,
3.15
and
3.16
, respectively to elucidate the rela-
tion of the input and the designed membership strength. Figure
3.17
shows the
output quadruple division's membership function.
The decision rules described in Fig.
3.12
can be perceived as linguistic rules in
fuzzy logic controller. The fuzzy inference mechanism system adopted is the most
commonly used Mamdani and Assilian [
20
] implication rules:
1. Represent the 'and' antecedent connective using min (intersection) opera-
tor; represent the 'or' antecedent connective using max (union) operator. Let
A
and
B
denote two fuzzy sets on the X universe, and x denotes any member
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