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Fig. 2.6
Membership functions of COSS terms “pressure at the high-pressure preheater inlet”
2.7 Analogues of Errors of the First and Second Kinds and A
Reliability Indicator for Models of Expert Evaluations of
Characteristics
2.7 Ana log ues of Errors of the F irst and Second Ki nds a nd A Relia bil ity Indicator for Model s
In [28] the quantity indicator of COSS quality is defined, namely, fuzziness
degree. Let us find analogues of errors of the first and second kinds and reliability
indicator for models
of
expert evaluations of characteristics.
Let
{
}
()
(
[
]
)
()
μ
x
≡
a
l
,
a
l
,
a
l
L
,
a
l
R
U
=
a
,
b
be COSS;
,
.
X
= μ
x
;
l
=
1
m
l
1
2
l
()
()
μ
x
μ
x
For membership functions
,
;
of the adjacent COSS terms
l
=
1
m
−
1
l
+
l
[
]
()
()
x
∈
U
:
0
<
μ
x
<
1
0
<
μ
x
<
1
there are uncertainty zones under
which
l
l
+
1
potency is equal to
l
a
. Based on characteristics of COSS membership functions
and concept of a probabilistic geometry, it is possible to consider
(
)
a
l
R
α
=
β
=
/
2
b
−
a
as analogues of errors of the first and second kinds for
X
l
l
l
X
, accordingly). Then
analogues of errors of the first and second kinds for models of expert evaluations
of characteristics will be referred to as
(analogues of errors of the second and first kinds for
+
1
{}
α
=
β
=
max
1
α
.
l
l
=
1
m
−
and analogue of a reliability indicator
(
)
2
V
=
1
−
α
.
2
⎛
l
R
⎞
⎧
a
⎫
⎜
⎜
⎝
⎟
⎟
⎠
V
=
1
−
max
.
⎩
⎨
⎭
⎬
(
)
2
b
−
a
l
=
1
m
−
1
