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In-Depth Information
Peter Hadjistoykov and the author extended the concept of an IFCM in two
directions: in [35] we introduced the concept of an IFCM with descriptors and in
[36]—Temporal IFCM.
Let
T
be a set of real numbers that will be interpreted as time-moments.
Let
C
={
C
1
,
C
2
,
·
,
C
n
}
be a set of cognitive units and for every
i
(
i
∈{
1
,
2
,
·
,
n
}
)
,
μ
C
(
C
i
)
and
ν
C
(
C
i
)
be the degrees of validity and non-validity of the cognitive unit
C
i
.
Extending the IFCM, we introduce the concept of Temporal Intuitionistic FCM
(TIFCM) as the pair
IFCM
=
C
(
T
),
E
(
T
)
,
where
C
(
T
)
={
C
i
, μ
C
(
C
i
,
t
), ν
C
(
C
i
,
t
)
|
C
i
∈
C
&
t
∈
T
}
is a TIFS and
E
(
T
)
=[
C, C,
{
μ
E
(
e
i
,
j
,
t
), ν
E
(
e
i
,
j
,
t
)
}]
,
is an Intuitionistic Fuzzy Index Matrix of incidence and for every
t
∈
T
,
i
,
j
∈
{
are degrees of validity and non-validity of the
oriented edge between neighbouring nodes
C
i
,
1
,
2
,
·
,
n
}
,
μ
E
(
e
i
,
j
,
t
)
and
ν
E
(
e
i
,
j
,
t
)
C
j
∈
C
of the temporal IF graph (see,
[6]) in time-moment
t
.
For every fixed time-moment
t
T
and for every two cognitive units
C
i
and
C
j
that are connected with an edge
e
i
,
j
, we can introduce different crite-
ria for correctness, e.g. if
C
i
∈
μ
C
(
C
i
,
), ν
C
(
C
i
,
)
≥
is higher than
C
j
(i.e.,
t
t
μ
C
(
C
j
,
t
), ν
C
(
C
j
,
t
)
), then
1 (top-down-max-min)
μ
C
(
C
i
,
t
), ν
C
(
C
i
,
t
)
∨
μ
E
(
e
i
,
j
,
t
), ν
E
(
e
i
,
j
,
t
)
≥
μ
C
(
C
j
,
t
), ν
C
(
C
j
,
t
)
;
2 (top-down-average)
μ
C
(
C
i
,
t
), ν
C
(
C
i
,
t
)
@
μ
E
(
e
i
,
j
,
t
), ν
E
(
e
i
,
j
,
t
)
≥
μ
C
(
C
j
,
t
), ν
C
(
C
j
,
t
)
;
3 (top-down-min-max)
μ
C
(
C
i
,
t
), ν
C
(
C
i
,
t
)
∧
μ
E
(
e
i
,
j
,
t
), ν
E
(
e
i
,
j
,
t
)
≥
μ
C
(
C
j
,
t
), ν
C
(
C
j
,
t
)
;
4 (bottom-up-max-min)
μ
C
(
C
i
,
t
), ν
C
(
C
i
,
t
)
∧
μ
E
(
e
i
,
j
,
t
), ν
E
(
e
i
,
j
,
t
)
≤
μ
C
(
C
j
,
t
), ν
C
(
C
j
,
t
)
;
5 (bottom-up-average)
μ
C
(
C
i
,
t
)ν
C
(
C
i
,
t
)
@
μ
E
(
e
i
,
j
,
t
), ν
E
(
e
i
,
j
,
t
)
≤
μ
C
(
C
j
,
t
), ν
C
(
C
j
,
t
)
;
6 (bottom-up-min-max)
μ
C
(
C
i
,
t
), ν
C
(
C
i
,
t
)
∨
μ
E
(
e
i
,
j
,
t
), ν
E
(
e
i
,
j
,
t
)
≤
μ
C
(
C
j
,
t
), ν
C
(
C
j
,
t
)
,
where for pairs
a
,
b
and
c
,
d
(
a
,
b
,
c
,
d
,
a
+
b
,
c
+
d
∈[
0
,
1
]
)
,
a
+
c
b
+
d
a
,
b
@
c
,
d
=
,
.
2
2
Other criteria are also possible. For example, all above criteria can be re-written
for the case, when they must be valid for any
t
∈
T
.
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