Information Technology Reference
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a
=
1
a
=
0
a
=
0
a
=
0
a
=
0
As
,
,
i
=
1
k
, we suppose that
,
. As
,
im
3
11
12
12
11
a
=
1
m
a
.
Let us denote a half-sum of a module integral of difference between related
right boundaries of membership functions of a set
a
=
1
=
1
,
i
=
1
k
, we suppose that
,
im
4
m
3
4
element
l
-th term and the
generalized model, on the one hand, and an module integral of difference between
related left boundaries of membership functions of a set
k
Ξ
(
)
k
Ξ
element
l
+
1
-th
l
=
1
m
−
1
term and the generalized model
, on the other hand, as information loss
within boundaries of
l
-th and
(
)
k
Ξ
-th terms between a set
element and its
l
+
1
generalized model.
Let us consider various cases of disposition of boundaries of membership
functions (Fig. 4.1) of the adjacent terms of set
i
-th element and boundaries
of membership functions of the same terms of the generalized model. Let us
determine information losses depending on the disposition of boundaries of
membership functions.
k
Ξ
Fig. 4.1
Boundaries of membership functions
a
>
a
a
>
a
, then loss of the information within the boundaries of
l
-
If
,
l
3
il
3
l
4
il
4
(
1
l
+
a
−
a
th and
-th terms is equal to square of trapezoid with base
,
l
3
il
3
a
−
a
and unit height, i.e.
l
4
il
4
1
(
)
a
−
a
+
a
−
a
.
(4.21)
l
3
il
3
l
4
il
4
2
(
)
a
<
a
a
<
a
l
+
1
If
,
, information loss on boundary of
-th terms is equal
l
3
il
3
l
4
il
4
a
−
a
a
−
a
to square of trapezoid with base
,
and unit height, i.e.
il
3
l
3
il
4
l
4
1
(
)
−
a
+
a
−
a
+
a
.
(4.22)
l
3
il
3
l
4
il
4
2