Information Technology Reference
In-Depth Information
expert undergoes while describing and estimating real objects within the scope of
relevant set of linguistic values of the characteristic considered. Therefore we
believe logical to assign the greatest weight coefficient to an element
(i.e. to
the model of expert evaluations of characteristic) with the minimum fuzziness
degree, and the least weight coefficient to an element
k
Ξ
k
with maximum
fuzziness degree. If fuzziness degrees of those elements are equal, weight
coefficients of those elements are considered equal.
Fuzziness degree of a characteristic expert evaluations model constructed in the
form of COSS is defined as follows:
Ξ
1
[
]
()
()
∫
ζ
=
f
μ
x
−
μ
x
dx
,
k
k
U
1
2
where
U
is a universal set (a subset on the real number line)
()
U
()
()
()
μ
x
=
max
μ
x
;
μ
x
=
max
μ
x
;
k
l
k
l
1
2
1
≤
l
≤
m
1
≤
l
≤
m
k
≠
k
1
()
()
f
.
Let us be limited to reviewing linear membership functions on a set
()
1
=
0
f
0
=
1
f
decreases, and
,
{
}
U
=
∪
x
∈
U
:
0
<
μ
x
<
1
l
=
1
m
,
l
l
()
f
x
=
1
−
x
and let us assume an integrand be equal
. It is the unique linear
()
()
function satisfying to conditions:
f
decreases,
f
0
=
1
,
f
1
=
0
. Then according
to [28]
=ζ
Let us calculate fuzziness degree for each element of set
U
/
2
U
.
k
and range all its
elements as per the following principle: the less fuzziness degree of an element is,
the higher its rank is. Without limiting its generality, we obtain, for example, a
conditional ordered series
Ξ
X
>
X
>
...
>
X
>
...
>
X
.
()
()
()
( )
1
1
i
k
Weight coefficients are computed by the formula (4.7).
If any elements have identical fuzziness degrees, determination weight
coefficients is made within the limits of schemes of §4.2.
If fuzziness degrees of all elements are equal, these elements are considered
equivalent, and weight coefficients
k
∑
=
ω
,
i
=
1
k
;
ω
=
1
i
i
i
1
equal, i.e
ω
=
1
/
k
,
i
=
1
k
.
i
