Information Technology Reference
In-Depth Information
If COSS's are constructed to the methods stated in §2.2 and 2.3 based on the
evaluations of a population of objects within the scope of some qualitative
characteristic given by
i
-th and
j
-th experts, the indexes defined above are
treated accordingly as distinction (similarity, consistency) indexes of criteria of
i
-
th and
j
-th experts.
If COSS's are constructed to the methods stated in § 2.2 and 2.3 based on the
expert evaluation of appearances of qualitative characteristics of
i
-th and
j
-th
populations of objects, the indexes defined above are treated accordingly as
distinction (similarity, consistency) indexes of appearance of this particular
qualitative characteristic.
Let us identify indexes of the general consistency of elements of set
k
with
Ξ
membership functions, accordingly
1
[
()
()
()
]
∫
min
μ
x
,
μ
x
,...,
μ
x
dx
1
l
2
l
kl
1
m
∑
κ
=
0
;
(3.3)
m
1
[
()
()
()
]
l
=
1
∫
max
μ
x
,
μ
x
,...,
μ
x
dx
1
l
2
l
kl
0
1
[
]
()
()
()
∫
min
μ
x
,
μ
x
,...,
μ
x
dx
1
l
2
l
kl
m
~
∏
∫
κ
=
0
.
m
1
(3.4)
[
]
()
()
()
l
=
1
max
μ
x
,
μ
x
,...,
μ
x
dx
1
l
2
l
kl
0
The index
is referred to as an additive index of consistency of elements of set
κ
~
is referred to as a multiplicative index of consistency of
Ξ
k
. The index
κ
elements of set
k
. The variation range of both indexes is a segment [0, 1]. If all
Ξ
elements of set
coincide, indexes are equal to unity. The additive index is
equal to zero, when membership functions of all terms have no crosscuts; and
multiplicative index is equal to zero, when membership functions of at least one
term have no crosscuts.
3.2 The Fuzzy Cl uster Ana lysi s of Set of Mo dels of Expert Characteristic
Ξ
k
3.2 The Fuzzy Cluster Analysis of Set of Models of Expert
Characteristic Evaluations
3.2 The Fuzzy Cl uster Ana lysi s of Set of Mo dels of Expert Characteristic
Building of fuzzy binary relations of similarity and conformity on set of models of
expert characteristic evaluations allows carrying out the fuzzy cluster analysis of
this set and, by that, to study its structural composition.
The Proposition 3.1.
[135] Fuzzy sets
R
—
R
with membership functions,
accordingly
(
)
~
(
)
~
(
)
(
)
l
ij
μ
X
,
X
=
κ
μ
X
,
X
=
κ
μ
X
,
X
=
κ
l
ij
μ
X
,
X
=
κ
R
i
j
ij
;
R
i
j
ij
;
R
i
j
;
R
i
j
,
1
3
4
2
