Information Technology Reference
In-Depth Information
Let us define index of distinction within the limits of
l
-th term of two elements as
loss of the information within the scope of
l
-th term between these elements
1
(
)
()
()
∫
d
μ
,
μ
=
μ
x
−
μ
x
dx
.
il
jl
il
jl
0
Index of similarity within the scope of
l
-th term
(
)
~
l
ij
κ −=
Let us define index of distinction of two elements as information loss between
these elements
1
d
μ
,
μ
.
il
jl
1
1
m
(
)
∑
∫
=
()
()
d
X
,
X
=
μ
x
−
μ
x
dx
.
(3.1)
i
j
il
jl
2
l
1
0
Index of similarity of two elements
~
(
)
κ
=
1
−
d
X
,
X
.
(3.2)
ij
i
j
Index of consistency of two elements within the scope of
l
-th term
1
[
]
()
()
∫
min
μ
x
,
μ
x
dx
il
jl
l
ij
κ
=
0
.
1
[
]
()
()
∫
max
μ
x
,
μ
x
dx
il
jl
0
Index of consistency of two elements
1
[
]
()
()
∫
min
μ
x
,
μ
x
dx
il
jl
1
m
∑
κ
=
0
.
ij
1
m
[
]
()
()
l
=
1
∫
max
μ
x
,
μ
x
dx
il
jl
0
All indexes vary from zero to unit.
While solving practical problems the selection of indexes of similarity or
consistency depends on a task set.
If it is necessary to determine degree of similarity between two elements of set
(of two COSS's) within the scope of terms with the greatest carriers, a
similarity index is recommended to use; and if within the scope of all terms
irrespective of their carriers, a consistency index is recommended to use.
If COSS's are constructed based on direct inquiries of
i
-th and
j
-th experts by
the methods stated in §2.4, 2.5, then indexes defined above are treated accordingly
as distinction (similarity, consistency) indexes of individual criteria of
i
-th and
j
-
th experts or description of characteristics.
k
Ξ
