<s>
A	O
fuzzy	B-General_Concept
control	I-General_Concept
system	I-General_Concept
is	O
a	O
control	O
system	O
based	O
on	O
fuzzy	O
logic	O
—	O
a	O
mathematical	O
system	O
that	O
analyzes	O
analog	O
input	O
values	O
in	O
terms	O
of	O
logical	O
variables	O
that	O
take	O
on	O
continuous	O
values	O
between	O
0	O
and	O
1	O
,	O
in	O
contrast	O
to	O
classical	O
or	O
digital	B-General_Concept
logic	O
,	O
which	O
operates	O
on	O
discrete	O
values	O
of	O
either	O
1	O
or	O
0	O
(	O
true	O
or	O
false	O
,	O
respectively	O
)	O
.	O
</s>
<s>
Although	O
alternative	O
approaches	O
such	O
as	O
genetic	B-Algorithm
algorithms	I-Algorithm
and	O
neural	B-Architecture
networks	I-Architecture
can	O
perform	O
just	O
as	O
well	O
as	O
fuzzy	O
logic	O
in	O
many	O
cases	O
,	O
fuzzy	O
logic	O
has	O
the	O
advantage	O
that	O
the	O
solution	O
to	O
the	O
problem	O
can	O
be	O
cast	O
in	O
terms	O
that	O
human	O
operators	O
can	O
understand	O
,	O
so	O
that	O
their	O
experience	O
can	O
be	O
used	O
in	O
the	O
design	O
of	O
the	O
controller	O
.	O
</s>
<s>
Fuzzy	B-General_Concept
systems	I-General_Concept
were	O
initially	O
implemented	O
in	O
Japan	O
.	O
</s>
<s>
Interest	O
in	O
fuzzy	B-General_Concept
systems	I-General_Concept
was	O
sparked	O
by	O
Seiji	O
Yasunobu	O
and	O
Soji	O
Miyamoto	O
of	O
Hitachi	O
,	O
who	O
in	O
1985	O
provided	O
simulations	O
that	O
demonstrated	O
the	O
feasibility	O
of	O
fuzzy	B-General_Concept
control	I-General_Concept
systems	I-General_Concept
for	O
the	O
Sendai	O
Subway	O
.	O
</s>
<s>
Their	O
ideas	O
were	O
adopted	O
,	O
and	O
fuzzy	B-General_Concept
systems	I-General_Concept
were	O
used	O
to	O
control	O
accelerating	O
,	O
braking	O
,	O
and	O
stopping	O
when	O
the	O
Namboku	O
Line	O
opened	O
in	O
1987	O
.	O
</s>
<s>
In	O
1987	O
,	O
Takeshi	O
Yamakawa	O
demonstrated	O
the	O
use	O
of	O
fuzzy	B-General_Concept
control	I-General_Concept
,	O
through	O
a	O
set	O
of	O
simple	O
dedicated	O
fuzzy	O
logic	O
chips	O
,	O
in	O
an	O
"	O
inverted	O
pendulum	O
"	O
experiment	O
.	O
</s>
<s>
Japanese	O
engineers	O
subsequently	O
developed	O
a	O
wide	O
range	O
of	O
fuzzy	B-General_Concept
systems	I-General_Concept
for	O
both	O
industrial	O
and	O
consumer	O
applications	O
.	O
</s>
<s>
Japanese	O
consumer	O
goods	O
often	O
incorporate	O
fuzzy	B-General_Concept
systems	I-General_Concept
.	O
</s>
<s>
Matsushita	O
vacuum	O
cleaners	O
use	O
microcontrollers	B-Architecture
running	O
fuzzy	O
algorithms	O
to	O
interrogate	O
dust	O
sensors	O
and	O
adjust	O
suction	O
power	O
accordingly	O
.	O
</s>
<s>
Canon	O
developed	O
an	O
autofocusing	O
camera	O
that	O
uses	O
a	O
charge-coupled	B-Algorithm
device	I-Algorithm
(	O
CCD	O
)	O
to	O
measure	O
the	O
clarity	O
of	O
the	O
image	O
in	O
six	O
regions	O
of	O
its	O
field	O
of	O
view	O
and	O
use	O
the	O
information	O
provided	O
to	O
determine	O
if	O
the	O
image	O
is	O
in	O
focus	O
.	O
</s>
<s>
The	O
camera	O
's	O
fuzzy	B-General_Concept
control	I-General_Concept
system	I-General_Concept
uses	O
12	O
inputs	O
:	O
6	O
to	O
obtain	O
the	O
current	O
clarity	O
data	O
provided	O
by	O
the	O
CCD	O
and	O
6	O
to	O
measure	O
the	O
rate	O
of	O
change	O
of	O
lens	O
movement	O
.	O
</s>
<s>
The	O
fuzzy	B-General_Concept
control	I-General_Concept
system	I-General_Concept
uses	O
13	O
rules	O
and	O
requires	O
1.1	O
kilobytes	O
of	O
memory	O
.	O
</s>
<s>
Other	O
applications	O
investigated	O
or	O
implemented	O
include	O
:	O
character	O
and	O
handwriting	B-Application
recognition	I-Application
;	O
optical	O
fuzzy	B-General_Concept
systems	I-General_Concept
;	O
robots	O
,	O
including	O
one	O
for	O
making	O
Japanese	O
flower	O
arrangements	O
;	O
voice-controlled	B-Application
robot	O
helicopters	O
(	O
hovering	O
is	O
a	O
"	O
balancing	O
act	O
"	O
rather	O
similar	O
to	O
the	O
inverted	O
pendulum	O
problem	O
)	O
;	O
rehabilitation	O
robotics	O
to	O
provide	O
patient-specific	O
solutions	O
(	O
e.g.	O
</s>
<s>
Work	O
on	O
fuzzy	B-General_Concept
systems	I-General_Concept
is	O
also	O
proceeding	O
in	O
North	O
America	O
and	O
Europe	O
,	O
although	O
on	O
a	O
less	O
extensive	O
scale	O
than	O
in	O
Japan	O
.	O
</s>
<s>
The	O
US	O
Environmental	O
Protection	O
Agency	O
has	O
investigated	O
fuzzy	B-General_Concept
control	I-General_Concept
for	O
energy-efficient	O
motors	O
,	O
and	O
NASA	O
has	O
studied	O
fuzzy	B-General_Concept
control	I-General_Concept
for	O
automated	O
space	O
docking	O
:	O
simulations	O
show	O
that	O
a	O
fuzzy	B-General_Concept
control	I-General_Concept
system	I-General_Concept
can	O
greatly	O
reduce	O
fuel	O
consumption	O
.	O
</s>
<s>
In	O
1995	O
Maytag	O
introduced	O
an	O
"	O
intelligent	O
"	O
dishwasher	B-Application
based	O
on	O
a	O
fuzzy	O
controller	O
and	O
a	O
"	O
one-stop	O
sensing	O
module	O
"	O
that	O
combines	O
a	O
thermistor	O
,	O
for	O
temperature	O
measurement	O
;	O
a	O
conductivity	O
sensor	O
,	O
to	O
measure	O
detergent	O
level	O
from	O
the	O
ions	O
present	O
in	O
the	O
wash	O
;	O
a	O
turbidity	O
sensor	O
that	O
measures	O
scattered	O
and	O
transmitted	O
light	O
to	O
measure	O
the	O
soiling	O
of	O
the	O
wash	O
;	O
and	O
a	O
magnetostrictive	O
sensor	O
to	O
read	O
spin	O
rate	O
.	O
</s>
<s>
Research	O
and	O
development	O
is	O
also	O
continuing	O
on	O
fuzzy	O
applications	O
in	O
software	O
,	O
as	O
opposed	O
to	O
firmware	B-Application
,	O
design	O
,	O
including	O
fuzzy	O
expert	B-Application
systems	I-Application
and	O
integration	O
of	O
fuzzy	O
logic	O
with	O
neural-network	B-Architecture
and	O
so-called	O
adaptive	O
"	O
genetic	B-Algorithm
"	O
software	O
systems	O
,	O
with	O
the	O
ultimate	O
goal	O
of	O
building	O
"	O
self-learning	O
"	O
fuzzy-control	O
systems	O
.	O
</s>
<s>
The	O
input	O
variables	O
in	O
a	O
fuzzy	B-General_Concept
control	I-General_Concept
system	I-General_Concept
are	O
in	O
general	O
mapped	O
by	O
sets	O
of	O
membership	O
functions	O
similar	O
to	O
this	O
,	O
known	O
as	O
"	O
fuzzy	O
sets	O
"	O
.	O
</s>
<s>
The	O
fuzzy	O
logic	O
based	O
approach	O
had	O
been	O
considered	O
by	O
designing	O
two	O
fuzzy	B-General_Concept
systems	I-General_Concept
,	O
one	O
for	O
error	O
heading	O
angle	O
and	O
the	O
other	O
for	O
velocity	O
control	O
.	O
</s>
<s>
Given	O
"	O
mappings	O
"	O
of	O
input	O
variables	O
into	O
membership	O
functions	O
and	O
truth	O
values	O
,	O
the	O
microcontroller	B-Architecture
then	O
makes	O
decisions	O
for	O
what	O
action	O
to	O
take	O
,	O
based	O
on	O
a	O
set	O
of	O
"	O
rules	O
"	O
,	O
each	O
of	O
the	O
form	O
:	O
</s>
<s>
From	O
three	O
to	O
seven	O
curves	O
are	O
generally	O
appropriate	O
to	O
cover	O
the	O
required	O
range	O
of	O
an	O
input	O
value	O
,	O
or	O
the	O
"	O
universe	B-Algorithm
of	I-Algorithm
discourse	I-Algorithm
"	O
in	O
fuzzy	O
jargon	O
.	O
</s>
<s>
Typical	O
fuzzy	B-General_Concept
control	I-General_Concept
systems	I-General_Concept
have	O
dozens	O
of	O
rules	O
.	O
</s>
<s>
In	O
practice	O
,	O
the	O
fuzzy	B-General_Concept
rule	I-General_Concept
sets	O
usually	O
have	O
several	O
antecedents	O
that	O
are	O
combined	O
using	O
fuzzy	O
operators	O
,	O
such	O
as	O
AND	O
,	O
OR	O
,	O
and	O
NOT	O
,	O
though	O
again	O
the	O
definitions	O
tend	O
to	O
vary	O
:	O
AND	O
,	O
in	O
one	O
popular	O
definition	O
,	O
simply	O
uses	O
the	O
minimum	O
weight	O
of	O
all	O
the	O
antecedents	O
,	O
while	O
OR	O
uses	O
the	O
maximum	O
value	O
.	O
</s>
<s>
Fuzzy	B-General_Concept
control	I-General_Concept
system	I-General_Concept
design	O
is	O
based	O
on	O
empirical	O
methods	O
,	O
basically	O
a	O
methodical	O
approach	O
to	O
trial-and-error	O
.	O
</s>
<s>
Consider	O
implementing	O
with	O
a	O
microcontroller	B-Architecture
chip	O
a	O
simple	O
feedback	O
controller	O
:	O
</s>
<s>
If	O
the	O
error	O
ranges	O
from	O
-1	O
to	O
+1	O
,	O
with	O
the	O
analog-to-digital	O
converter	O
used	O
having	O
a	O
resolution	O
of	O
0.25	O
,	O
then	O
the	O
input	O
variable	O
's	O
fuzzy	O
set	O
(	O
which	O
,	O
in	O
this	O
case	O
,	O
also	O
applies	O
to	O
the	O
output	O
variable	O
)	O
can	O
be	O
described	O
very	O
simply	O
as	O
a	O
table	O
,	O
with	O
the	O
error	O
/	O
delta	O
/	O
output	O
values	O
in	O
the	O
top	O
row	O
and	O
the	O
truth	O
values	O
for	O
each	O
membership	O
function	O
arranged	O
in	O
rows	O
beneath	O
:	O
</s>
<s>
Suppose	O
this	O
fuzzy	B-General_Concept
system	I-General_Concept
has	O
the	O
following	O
rule	O
base	O
:	O
</s>
<s>
As	O
an	O
example	O
,	O
consider	O
an	O
anti-lock	O
braking	O
system	O
,	O
directed	O
by	O
a	O
microcontroller	B-Architecture
chip	O
.	O
</s>
<s>
The	O
microcontroller	B-Architecture
has	O
to	O
make	O
decisions	O
based	O
on	O
brake	O
temperature	O
,	O
speed	O
,	O
and	O
other	O
variables	O
in	O
the	O
system	O
.	O
</s>
<s>
The	O
above	O
example	O
demonstrates	O
a	O
simple	O
application	O
,	O
using	O
the	O
abstraction	B-Application
of	O
values	O
from	O
multiple	O
values	O
.	O
</s>
<s>
Adding	O
additional	O
sophistication	O
to	O
this	O
braking	O
system	O
,	O
could	O
be	O
done	O
by	O
additional	O
factors	O
such	O
as	O
traction	O
,	O
speed	O
,	O
inertia	O
,	O
set	O
up	O
in	O
dynamic	O
functions	O
,	O
according	O
to	O
the	O
designed	O
fuzzy	B-General_Concept
system	I-General_Concept
.	O
</s>
<s>
Then	O
the	O
formula	O
Cold(r )	O
→	O
High(t )	O
is	O
true	O
for	O
any	O
t	O
and	O
therefore	O
any	O
t	O
gives	O
a	O
correct	O
control	O
given	O
r	O
.	O
A	O
rigorous	O
logical	O
justification	O
of	O
fuzzy	B-General_Concept
control	I-General_Concept
is	O
given	O
in	O
Hájek	O
's	O
book	O
(	O
see	O
Chapter	O
7	O
)	O
where	O
fuzzy	B-General_Concept
control	I-General_Concept
is	O
represented	O
as	O
a	O
theory	O
of	O
Hájek	O
's	O
basic	O
logic	O
.	O
</s>
<s>
In	O
Gerla	O
2005	O
another	O
logical	O
approach	O
to	O
fuzzy	B-General_Concept
control	I-General_Concept
is	O
proposed	O
based	O
on	O
fuzzy	O
logic	O
programming	O
:	O
Denote	O
by	O
f	O
the	O
fuzzy	O
function	O
arising	O
of	O
an	O
IF-THEN	O
systems	O
of	O
rules	O
.	O
</s>
<s>
The	O
interpretation	O
of	O
this	O
predicate	O
in	O
the	O
least	O
fuzzy	O
Herbrand	O
model	O
of	O
P	O
coincides	O
with	O
f	O
.	O
This	O
gives	O
further	O
useful	O
tools	O
to	O
fuzzy	B-General_Concept
control	I-General_Concept
.	O
</s>
<s>
System	O
identification	O
can	O
be	O
realized	O
with	O
precise	O
mathematical	O
equations	O
or	O
with	O
Fuzzy	B-General_Concept
rules	I-General_Concept
.	O
</s>
<s>
Using	O
Fuzzy	O
logic	O
and	O
ANFIS	B-Algorithm
systems	O
(	O
Adaptive	O
network	O
based	O
fuzzy	O
inference	O
system	O
)	O
for	O
creating	O
the	O
forward	O
model	O
for	O
a	O
domain	O
has	O
many	O
disadvantages	O
.	O
</s>
<s>
The	O
output	O
of	O
the	O
ANFIS	B-Algorithm
system	O
is	O
n't	O
providing	O
correct	O
information	O
,	O
but	O
only	O
a	O
Fuzzy	O
set	O
notation	O
,	O
for	O
example	O
 [ 0 , 0.2 , 0.4 , 0 ] 	O
.	O
</s>
<s>
Fuzzy	B-General_Concept
control	I-General_Concept
systems	I-General_Concept
are	O
suitable	O
when	O
the	O
process	O
complexity	O
is	O
high	O
including	O
uncertainty	O
and	O
nonlinear	O
behavior	O
,	O
and	O
there	O
are	O
no	O
precise	O
mathematical	O
models	O
available	O
.	O
</s>
<s>
Successful	O
applications	O
of	O
fuzzy	B-General_Concept
control	I-General_Concept
systems	I-General_Concept
have	O
been	O
reported	O
worldwide	O
mainly	O
in	O
Japan	O
with	O
pioneering	O
solutions	O
since	O
80s	O
.	O
</s>
