Information Technology Reference
In-Depth Information
1
∩
k
i
(
)
(
)
2
1
1
2
1
0
x
=
x
,
x
;
i
i
=
1
2
∩
k
i
(
)
(
)
1
2
2
1
2
2
2
x
,
x
=
x
,
x
;
i
i
=
1
……………………
(
∩
k
i
)
(
)
1
1
2
x
,
=
x
,
x
.
m
im
im
=
1
If
∩
m
l
(
)
[]
1
2
0
=
x
,
x
,
l
l
then COSS term-set membership functions are transformed to characteristic
functions of intervals
=
1
(
)
1
2
(
)
l
xx
, then instead
of intersection operation,
r
-composition of intervals operation [124] is applied.
Operation of
r
-composition of intervals is introduced through union and
intersection operations as follows:
x
,
x
,
l
=
1
m
. If one of intervals
1
2
,
=
Ø
l
l
l
(
)
[
(
)
(
)
]
⎛
k
⎞
∪
∩∩
r
x
1
,
x
2
=
x
1
,
x
2
...
x
1
,
x
2
;
⎜
⎝
⎟
⎠
i
i
i
i
i
i
1
1
k
−
r
+
1
k
−
r
+
1
i
=
1
i
≠
...
≠
i
1
k
−
r
+
1
k
(
)
[
(
)
(
)
]
⎛
⎞
∩
∪∪
1
2
1
2
1
2
r
x
,
x
=
x
,
x
...
x
,
x
.
⎜
⎝
⎟
⎠
i
i
i
i
i
i
i
=
1
1
1
r
r
i
≠
...
≠
i
1
r
The selection of
is obvious because the "most representative" expert
should prefer an evaluation, which is remote from extreme evaluations and
occupying "middle" position. If
r
≈
k
/
2
(
) (
)
(
)
1
2
1
2
, or
∃
l
:
x
,
x
∩
x
,
x
=
a
,
b
≠
φ
l
l
l
−
1
l
−
1
l
l
(
) (
)
(
)
(
)
(
)
1
2
1
2
x
,
x
1
2
1
2
x
1
,
x
xx
∩
,
x
,
x
=
a
,
b
≠
Ø
, then instead of intervals
,
,
l
−
l
−
1
l
l
l
l
l
+
1
l
+
1
l
l
(
)
1
2
x
1
,
x
the following intervals are considered, accordingly
(
l
+
l
+
1
) (
)
~
~
~
~
(
)
(
)
(
) (
)
1
2
1
2
x
1
,
x
2
=
x
1
,
x
2
\
a
,
b
x
,
x
=
x
,
x
\
a
,
b
l
−
1
l
−
1
l
−
1
l
−
1
l
l
;
l
l
l
l
l
l
~
~
(
)
(
) (
)
x
1
,
x
2
=
x
1
,
x
2
\
a
,
b
.
l
+
1
l
+
1
l
+
1
l
+
1
l
l
(
)
[
]
1
2
x
,
x
U
=
a
,
b
Let us assume that intervals
typical for COSS terms are
defined. Let us consider that the fuzzy numbers corresponding to COSS terms are
Λ
and
l
l
()
()
-numbers, and the side condition (1*) is satisfied for functions
L
x
,
. Let
R
x
()
μ
x
us denote membership functions of terms
X
with
.
l
Then with even
m
