Information Technology Reference
In-Depth Information
•
The antecedent (
S
is
q
i
) calculates the degree of activation of the state
q
i
in
the instant of time
t
, i.e.,
s
i
[
t
]
(
)
. Note that the FFSM cannot remain in the state
q
i
if it is not in this state previously.
t
The antecedents (
u
1
is
A
u
1
)
(
u
n
u
is
A
u
n
u
) are the constraints over the input
variables to remain in the state
q
i
. Each
A
u
i
is a set of linguistic terms whose
members are joined by a disjunctive operator, e.g.,
A
u
1
=
•
,...,
A
u
1
∨
A
u
1
.
•
The antecedent (
d
i
is
T
st ay
i
) is a temporal constraint that calculates the member-
ship degree of the duration of the state
q
i
(
d
i
, which is defined as the time that
s
i
>
0) to the linguistic label
T
st ay
i
, which is the maximum time that the system
is expected to remain in state
q
i
. In Fig. 11.2, can be seen an example of this
linguistic label.
•
Finally, the consequent of the rule is the next value of the state activation vector
S
. It consists of a vector with a zero in all of its components except in
s
i
,
where it has a one.
[
t
+
1
]
The generic expression of a rule to change form state
q
i
to the state
q
j
(
R
ij
)is
formulated as follows: IF (
S
(
u
1
is
A
u
1
)
is
A
u
n
u
)
[
t
]
is
q
i
)
∧
∧...∧
(
u
n
u
∧
(
d
i
is
T
change
i
)THEN
S
[
t
+
1
]
is
q
j
,where:
•
The antecedent (
S
is
q
i
) calculates the degree of activation of the state
q
i
in the
instant of time
t
, i.e.,
s
i
(
[
t
]
. Note that the FFSM cannot change from the state
q
i
to the state
q
j
if it is not in this state previously.
t
)
The antecedents (
u
1
is
A
u
1
)
(
u
n
u
is
A
u
n
u
) are the constraints over the input
variables to change from state
q
i
to the state
q
j
. Each
A
u
i
is a set of linguistic
terms whose members are joined by a disjunctive operator, e.g.,
A
u
1
=
•
,...,
A
u
1
∨
A
u
1
.
•
The antecedent (
d
i
is
T
change
i
) is a the temporal constraint which calculates the
membership degree of the duration of the state
q
i
(
d
i
, which is defined as the
time that
s
i
>
0) to the linguistic label
T
change
i
, which is the minimum time that
the signal is expected to remain in the state
q
i
before changing to the state
q
j
.In
Fig. 11.2, can be seen an example of this linguistic label.
•
Finally, the consequent of the rule is the next value of the state activation vector
S
. It consists of a vector with a zero in all of its components except in
s
j
,
where it has a one.
[
t
+
1
]
To calculate the next value of the state activation vector (
S
[
t
+
1
]
), a weighted aver-
age using the firing degree of each rule
k
(
ω
k
) is computed as defined in Eq. 11.1:
⎨
#
Rules
k
=
1
ω
k
·
(
s
1
,...,
s
n
)
k
#
Rules
k
=
1
ω
k
#
Rules
k
=
1
ω
k
=
0
if
S
[
t
+
1
]=
(11.1)
⎩
#
Rules
k
=
1
ω
k
=
0
S
[
t
]
if
where (
ω
k
) is calculated using the minimum for the AND operator (
∧
) and the maxi-
mum for the OR operator (
in
R
ii
to make more difficult the change of
state, which makes the FFSM more robust against spurious in the input. Moreover,
we used
∨
). We used
∨
∧
in
R
ij
to define the conditions to change more sharply.
