Information Technology Reference
In-Depth Information
Let
S
k
,
l
(
a
C
k
,
O
i
,
a
C
k
,
O
j
)
(
a
C
l
,
O
i
,
be the number of cases in which
R
and
R
are simultane
ou
sly satisfied. Let
S
k
,
l
a
C
l
,
O
j
)
be the number of cases in which
R
(
a
C
k
,
O
i
,
a
C
k
,
O
j
)
and
R
(
a
C
l
,
O
i
,
a
C
l
,
O
j
)
are simultaneously satisfied.
Obviously,
n
(
n
−
1
)
S
k
,
l
+
S
k
,
l
≤
.
2
Now, for every
k
,
l
, such that 1
≤
k
<
l
≤
m
and for
n
≥
2, we define
S
k
,
l
S
k
,
l
μ
C
k
,
C
l
=
2
)
,ν
C
k
,
C
l
=
2
)
.
n
(
n
−
1
n
(
n
−
1
Therefore,
μ
C
k
,
C
l
,ν
C
k
,
C
l
is an IFP. Now, we can construct the IM
C
1
...
C
m
C
1
μ
C
1
,
C
1
,ν
C
1
,
C
1
...
μ
C
1
,
C
m
,ν
C
1
,
C
m
,
.
.
.
C
m
μ
C
m
,
C
1
,ν
C
m
,
C
1
...
μ
C
m
,
C
m
,ν
C
m
,
C
m
that determine the degrees of correspondence between criteria
C
1
,...,
C
m
.
Let
α, β
∈[
0
,
1
]
be given, so that
α
+
β
≤
1. We say that criteria
C
k
and
C
l
are
in
•
(α, β)
-positive consonance, if
μ
C
k
,
C
l
>α
and
ν
C
k
,
C
l
<β
;
•
(α, β)
-negative consonance, if
μ
C
k
,
C
l
<β
and
μ
C
k
,
C
l
>α
;
•
(α, β)
-dissonance, otherwise.
The method can be used for prediction.
Let the IM
A
be given and let criterion
D
(e.g., one of the criteria
C
1
,...,
C
m
)
be fixed. Let us reduce IM
A
to the IM
O
1
...
O
k
...
O
l
...
O
n
C
1
a
C
1
,
O
1
...
a
C
1
,
O
k
...
a
C
1
,
O
l
...
a
C
1
,
O
n
.
.
.
.
.
.
.
.
B
=
C
i
a
C
i
,
O
1
...
a
C
i
,
O
k
...
a
C
i
,
O
l
...
a
C
i
,
O
n
.
.
.
.
.
.
.
.
C
p
a
C
p
,
O
1
...
a
C
p
,
O
k
...
a
C
p
,
O
l
...
a
C
p
,
O
n
D
b
D
,
O
1
...
b
D
,
O
k
...
b
D
,
O
l
...
b
D
,
O
n
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