Information Technology Reference
In-Depth Information
Chapter 4
Model-Building Techniques of the Generalized
Characteristic Expert Evaluation Models
4.1 The Generalized Model of Characteristic Expert
Evaluations Based on the Least Square Method
4.1 The G eneralize d Model of Characteristic Ex pert Eval uatio ns
The expert evaluations theory has formulated the optimum condition of group
sampling as per Pareto [135]. This condition means that if
(
)
R
=
F
R
,
R
,...,
R
is
1
2
R
,
R
,...,
R
the group ranking, which is function of individual rankings
, then
1
2
k
k
∩
R
⊆
R
⊆
∪
R
.
n
n
n
=
1
n
=
1
{
}
Let
be models of expert evaluations of
qualitative characteristic or expert description in linguistic terms of physical
values of
qua
ntitative characteristic with membership functions of term-sets
()
, where
X
;
Ξ
k
=
X
i
;
i
=
1
k
i
=
1
k
()
(
)
{
}
. Let us construct generalized model of
X
expert evaluations of a property based on the models
,
μ
x
≡
a
il
,
a
il
,
a
il
L
,
a
il
R
μ
x
,
l
=
1
m
il
il
1
2
X
[COSS with
()
(
)
()
l
l
l
L
l
R
f
x
=
a
,
a
,
a
,
a
membership functions of term-set
].
Let us formulate Pareto condition for the optimum generalized model of expert
evaluations of a qualitative characteristic or expert description of values of
quantitative characteristic in the linguistic terms, which is constructed on the basis
of models
f
l
x
,
1
2
l
X
k
k
∩
X
⊆
X
⊆
∪
X
.
i
i
i
=
1
i
=
1
or
[
()
()
()
]
()
≤
min
μ
x
,
μ
x
,...,
μ
x
≤
f
x
1
l
2
l
kl
l
i
=
1
k
[
()
()
()
]
[
]
≤
max
μ
x
,
μ
x
,...,
μ
x
;
∀
x
∈
0
,
l
=
1
m
.
(4.1)
1
l
2
l
kl
i
=
1
k
Let us assume [150] that membership functions of a term-set of the generalized
characteristic expert evaluations model is related to the same class of functions as
