CHINESE
JOURNAL
Aug.
2006
OF
ENGINEERING
MATHEMATICS
Vo!.
23
No.
4
Article
ID:
1005-3085(2006)04-0599-ω
Incremental
Construction
of
Minimal
Acyclic
Deterministic
Fu
zzy
Finite
Automaton
HU
Hong-li,
MO
Zhi-wen
(College ofMathematics and Software Science
, Sichuan Normal University,
Che
吨
du
610066)
Abstract:
We
presented a new semi-incremental algorithm, which combines with properties of acyclic
deterministic fuzzy automata. Because the algorithm is related with fuzzy membership
,
we
present some novel functions which make the new algorithm
different
仕
om
general
algorithm.
It
can be applied to multi-incoming (transitions) states by applying build-
imitate state. So the new semi-incremental algorithm
is
more useful and practical. The new
algorithm
is
composed of two parts: adding fuzzy strings to minimal acydic deterministic
fuzzy finite
state
automata (ADFFAs) and minimizing the resulting automata. Because
some novel functions are applied in the algorithm
for
adding fuzzy stings
to
ADFFAs. The
resulting automaton of the algorithm
is
still deterministic and
is
not added more
than
one
fuzzy string to automaton.
Keywords:
acyclic deterministic fuzzy finite automaton; fuzzy strings; semi-incremental algorithm;
build-imitate state; unnecessary-membership
state
Classification:
AMS(2000) 68Q19
CLC
number:
T312
Document
code:
A
1
Introduction
Fu
zzy
set
theory
has
received considerable
attention
since
its
inception[1,
2j.
A
wide
飞
rariety
of
tools
have
been
developed
basing
on
the
notion
of
fuzzy
membership
function.
for
example
,
there
has
been
an
increased
interest
in
combing fuzzy
systems
with
finite
automata.
The
notion
of
fuzzy
automata
was
introduced
by
Lee
and
Wee[3,
4j.
80me
basic
properties
of
fuzzy
automata
can
be
found
in
[5
，
6
，可.
As a design
tool
,
the
fuzzy
automata
should
be
best
, if
it
is
minima
l.
In
this
p
也.p
er
，
we
present
two
algorithms
for
adding
fuzzy
strings
to
acyclic
deterministic
fuzzy finite
automata
(ADFFAs)
and
minimizing
the
resulting
automata
,
semi-incremental
techniques
，町咆
used
to
constrict
minimal
ADFFAs.
The
semi-incremental
algorithm
is used
in
minimal
condition
, so
it
is
named
semi-incrementa
l.
This
was applied
in
some
papers[8,
9j
,
but
these
papers
only considered
the
general
automata.
In
this
paper
,
in
order
to
constricting
minimal
acyclic
deterministic
fuzzy finite
state
automata
, we would combine
the
general
semi-incremental techniques
with
fuzzy
nature.
Previous
work
on
the
semi-incremental
algorithm
is
not
applicable
to
the
multi-incoming
(transitions)
stat
臼
(in
some
pap
町
they
are
named
confuse states)[lO-13j. Nevertheless,
the
multi-incoming
(transitions)
states
usually exist, especially
in
minimal
automata.
The
new
semi-incremental
algorithm
given
in
this
paper
can
be
applied
to
multi-incoming
(transitions)
states.
80
the
new
algorithm
is
more
general
and
easier
to
implement.
Received date:
200
4-0
4-
12.
Biography:
Hu
Hongli
(Born
in
197η
，民
male
，
Master.
Re
search
field:
fuzzy
theory,
rou
也
h
theory and
finite
automaton.
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