Information Technology Reference
In-Depth Information
Ranges of values of quantitative characteristics
X
can be non-enumerable sets
of points
R
of the real values line.
Using expert information we construct COSS with names
X
. If growth of
characteristic
X
is accompanied with growth of characteristic
Y
, then «very
small value of characteristic
X
», “small value of characteristic
X
", "average
value of characteristic
X
", "large value of characteristic
X
", "very large value
j
()
μ
x
of characteristic
i
are their membership
functions. If growth of characteristic
X
is accompanied by decreasing of
characteristic Y, then “very great value of characteristic
X
“ are COSS terms, and
,
=
1
ij
X
", "great value of
characteristic
X
"," average value of characteristic
X
", "small value of charac-
()
μ
x
teristic
X
", "very small value of characteristic
X
” are COSS terms, and
,
ij
i
=
1
are their membership functions.
Let us denote values of characteristics
x
,
n
X
for
n
-th object,
n
=
1
N
with
and degrees of a membership of these values to COSS terms named
X
- with
()
n
j
μ
x
i
=
1
j
=
1
l
n
=
1
N
,
,
,
.
ij
X
Let
be levels of the verbal scales applied to an evaluation of characteristics
lv
X
,
. Levels are arranged in ascending order of manifestation inten-
sity of relevant characteristic, if its growth is accompanied with
Y
growth, and in
decreasing order if its growth is accompanied with
Y
decrease.
Let us construct
v
=
l
+
1
k
k
−
l
COSS's named
X
, having related term-sets
X
, and
lv
()
[]
μ
x
membership functions
.
U
=
0
is selected as universal COSS sets. Fuzzy
lv
~
()
μ
are re-
ferred to as evaluations of objects. Let us denote an evaluation of
n
-th object
within the limits of characteristic
x
numbers
,
l
=
1
m
,
v
=
l
+
1
k
or their membership functions
lv
lv
v
~
()
(
)
n
v
n
v
n
v
n
vL
n
vR
μ
x
≡
a
,
a
,
a
,
a
X
with
n
v
and
.
1
2
~
()
n
v
n
v
μ
x
Fuzzy number
with membership function
is equal to one of fuzzy
~
numbers
,
l
=
1
m
,
v
=
l
+
1
k
.
v
lv
(
)
=
i
the function which
equal to '1' if an evaluation of
n
-th object within the limits of characteristic
n
v
1
Let us denote with
δ
i
x
,
n
=
1
N
,
v
=
l
+
1
k
,
X
~
=
i
, and equal to zero if an evaluation of
n
-th object
within the limits of characteristic
is fuzzy number
,
1
iv
~
p
≠
i
X
is fuzzy number
,
p
=
1
,
.
pv
k
∑
=
ω
ω
weight coefficients of estimated char-
acteristics. Calculate the following coefficients:
=
1
Let us denote with
,
j
=
1
k
,
j
j
j
1
