Information Technology Reference
In-Depth Information
The sets
{
}
{
}
{
}
==
−
of characteristic
X
linguistic to be applied to estimate the characteristic
considered, are formulated. After that, the experts are offered to estimate (or to
describe) this characteristic sequentially within the limits of each formulated sets
of its linguistic values.
Let
T
X
,
X
,
T
Y
,
Y
,
Y
,
...,
T
=
Z
,
Z
,...,
Z
1
1
2
2
1
2
3
n
1
1
2
n
{
}
{
}
{
}
==
−
are COSS term-sets constructed within the limits of these sets based on the
information obtained from each of
k
experts. Let us denote a model of expert
evaluations of characteristic
X
by
p
-th expert within the limits of term-set
T
X
,
X
,
T
Y
,
Y
,
Y
,
...,
T
=
Z
,
Z
,...,
Z
1
1
2
2
1
2
3
n
1
1
2
n
T
(COSS of
p
-th expert with a term-set
T
), with
P
P
i
−=
and the generalized model of expe
rt ev
aluations of characteristic
X
within the
limits of term-set
,
i
1
n
1
p
=
1
k
T
wit
h
P
,
. Let us denote fuzziness degree of the
i
=
1
n
−
1
()
P
wi
th
i
=
1
n
−
1
model
ξ
T
,
, and index of the general consistency of models
with
k
.
For a consistency index, we construct COSS with universal set [0.1], terms
"low", "high" and membership functions of terms
P
P
,
p
=
1
k
()
()
μ
x
,
μ
x
, without limiting a
1
2
() (
)
() (
)
μ
x
≡
0
0
25
;
0
0
50
μ
x
≡
0
75
;
1
0
25
;
0
generality, for example,
. For
a fuzziness degree we construct COSS with universal set [0; 0.5], terms "small",
"big" and membership functions of terms
,
1
2
() ()
η
x
,η
x
, without limiting a
1
2
() (
)
() (
)
η
x
≡
0
0
20
;
0
0
20
η
x
≡
0
40
;
0
50
;
0
20
;
0
generality, for example,
.
Let us calculate, within the limits of all sets of linguistic values, the
characteristic of membership value of fuzzi
ness d
egrees of the generalized models
to the term "small" —
,
1
2
[
]
()
η
ξ
T
=
ni
, and membership v
alues
of
consistency indexes of experts' models to the term "high" —
,
1
−
1
1
1
()
i
μ
k
i
=
1
n
−
1
,
.
2
Let us define
{
[
()
]
()
}
ηθ
Then, the set of characteristic linguistic values is considered an optimum set
(Fig. 4.2), if
=
min
ξ
T
,
μ
k
,
i
=
1
n
−
1
i
1
1
2
i
θ
=
max
1
θ
.
j
i
1
≤
≤
−
i
n
