Information Technology Reference
In-Depth Information
•
The overall system output:
D
1
(
D
2
(
(
)=
)
∨
)=(
α
∧
(
))
∨
(
α
∧
(
)))
D
d
d
d
D
1
d
D
2
d
1
2
•
Any defuzzification method to obtain a deterministic control action.
In our case we have already formal representation of rule-base as
R
SD
,
R
SD
,
R
SD
,or
R
t
SD
, so we do not construct these relations, they are given by experts. If
D
2
coin-
sides with
D
1
, in particular case, and
S
1
,
S
2
and
s
0
=
S
p
are estimated by linguistic
terms (Table 25.1) and their numerical equavalent (Table 25.3), the firing levels of
the rules and individual rule outputs are substituted by the following expressions:
D
1
=(
D
1
.If
S
1
and
S
2
are fuzzy sets
(see Table 25.5) and
S
p
is a singleton, a fuzzification is a necessary step of Mam-
dani case. If
S
p
is a triangle or trapezoidal fuzzy set, max and min operations are
used to find the individual rule outputs. Thus, a step with firing levels of the rules
is, in general, calculated using max and min operators and this as usually (see, for
example, fuzzy Matlab Toolbox) predefined in fuzzy control systems, mostly using
Mamdani and TSK inference process.
,
D
1
=(
D
1
∨
S
p
∧
R
S
1
D
1
)
S
p
∧
R
S
2
D
1
)
and
D
=
25.5
Simulation with Fuzzy Markup Language
We have done a simulation of proposed approach with the help of Fuzzy Markup
Language (FML) [1, 2, 31]. Fuzzy Markup Language is a XML-based domain-
specific language proposed by Acampora and Loia [2] whose main aim is to model
fuzzy systems by directly dealing with fuzzy concepts, fuzzy rules and fuzzy infer-
ence engines [8]. In the last years, FML (Fuzzy Markup Language) is emerging as
one of the most efficient and useful language to define a fuzzy control thanks to its
capability of modeling Fuzzy Logic Controllers in a human-readable and hardware
independent way, i.e., the so-called Transparent Fuzzy Controllers (TFCs) [3]. In
particular, it is used to model two well-known kind of fuzzy controllers: Mamdani
and Takagi-Sugeno-Kang (TSK).
We show how FML mechanism can be adjusted to suspect the RD [1]. Due to
the discusion from Section 25.4.2 some adjustments of FML to the given problem
are needed.
Using results discussed in the Section 25.4.1, remarks from the Section 25.4.2 the
rule-base of six input variables (wheezing, breathlessness, anosmia, fever, sinusitis,
chronic otitis) and two output variables (Bronchitis and Pneumonia) is presented as
it is shown in the Figure 25.1.
Results of execution of FML under
S
p
(see (25.9)) for
d
1
(Bronchitis) is presented
in the Figure 25.2.
In the Listing 25.1 a portion of the FML-based fuzzy controller to suspect the RD
is presented.
