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4.4 Buil di ng of t he G eneralize d Model of Characteristic Ex pert Eval uati
ons
4.4 Building of the Generalized Model of Characteristic Expert
Evaluations Based on the Minimum Information Loss
{
}
4.4 Buil di ng of t he G eneralize d Model of Characteristic Ex pert Eval uati
ons
Let
()
i
=
1
k
X
= μ
x
,
l
=
1
m
k
(models of expert
evaluations of qualitative characteristic or expert description of quantitative
characteristic physical values, in linguistic terms),
,
be elements of set
Ξ
i
il
()
(
)
il
il
il
L
il
R
μ
x
≡
a
,
a
,
a
,
a
.
Let us denote the generalize
d m
odel within the limits of eleme
nts
of set
il
1
2
k
Ξ
{
()
(
)
()
}
l
l
l
L
l
R
f
x
=
a
,
a
,
a
,
a
X
=
f
x
,
l
=
1
m
l
=
1
m
defined as COSS
,
,
.
l
1
2
l
X
and
X
of set
k
In §3.1 the distinction index of two elements
Ξ
with
{
()
}
{
()
}
μ
x
,
l
=
1
m
μ
x
,
l
=
1
m
membership functions
,
,
i
=
1
k
,
j
=
1
k
,
jl
il
X
and
X
of set
accordingly, or information loss between elements
Ξ
k
1
m
(
)
1
()
()
∑
∫
=
d
X
,
X
=
μ
x
−
μ
x
dx
i
j
il
jl
2
l
1
0
is defined.
By analogy to this definition, let us introduce
defi
nition of information loss
between
{
()
}
X
=
f
x
,
l
=
1
m
generalized
model
and
an
element
l
{
}
()
X
= μ
x
,
l
=
1
m
i
=
1
k
,
of set
k
, i.e.
Ξ
i
ii
1
m
1
(
)
()
()
∑
∫
=
d
X
,
X
=
μ
x
−
f
x
dx
.
i
il
l
2
Let us denote average value of information losses between elements of set
l
1
0
Ξ
k
and
the generalized model
1
k
(
)
∑
=
σ
=
d
X
,
X
,
i
=
1
k
.
i
k
As information loss occurred while constructing the generalized model within the
scope of the set
i
1
k
.
Let us consider that fuz
zy
numbers with membership func
tion
s
()
(
Ξ
()
(
)
)
il
il
il
L
il
R
l
l
l
L
l
R
μ
x
≡
a
,
a
,
a
,
a
f
x
=
a
,
a
,
a
,
a
l
=
1
m
i
=
1
k
,
,
,
,
il
1
2
l
1
2
k
corresponding to term-sets of set
elements and to term-set of the generalized
model, are
T
-numbers or normal triangular numbers,
Ξ
[]
U
.
Let us introduce new parameters of membership functions of term-sets of set
k
=
0
elements and membership functions of term-set of the generalized model,
which are abscissas of breakpoints of graphs of these membership functions [150]:
Ξ
il
il
L
,
il
,
il
,
il
il
R
,
a
=
a
−
a
a
=
a
a
=
a
a
=
a
+
a
il
1
1
il
2
1
il
3
2
il
4
2
l
l
L
l
l
a
=
a
l
+
a
l
R
.
a
=
a
−
a
,
a
=
a
,
a
=
a
,
l
1
1
l
2
1
l
3
2
l
4
2
