Civil Engineering Reference
In-Depth Information
∑
(
)
(
)
where
K
=
p
X
p
X
is the
degree of confl ict
between two
1
p
2
q
Xp
∩=
Xq
φ
sources of evidence. The denominator (1
K
) is a normalization factor,
which standardizes the effect of confl icting evidence on aggregation. The
DS rule of combination has interesting characteristics, e.g. the DS rule of
combination
−
⊕
is both
commutative
(i.e.
p
⊕
q
=
q
⊕
p
) and
associative
(i.e.
p
). This prop-
erty makes the DS rule of combination fl exible to update the evidence,
as more information is provided, but the order of the evidence is not
important.
A hypothetical example for data fusion of seismic damage classifi cation
is provided below. Two experts, decision makers DM
i
(
i
s
⊕
(
p
⊕
q
)
=
(
s
⊕
p
)
⊕
q
), but not
idempotent
(i.e.
p
⊕
p
≠
1, 2), have evalu-
ated a bridge damage during an earthquake reconnaissance. The damage
classifi cation used is C
j
(
j
=
=
1, 2, 3, 4), where C
1
=
none, C
2
=
medium, C
3
=
severe, and C
4
collapse damage states. The three experts' assessment and
bpa
are summarized below:
=
()
=
(
)
=
DM
p
C
040
.;
p
C
, ,
C
C
04
.
1
1
1
1
1
2
3
()
=
(
)
=
DM
p
C
030
.;
p
C
,
C
02
.
2
2
2
2
2
3
Both decision makers' assigned
bpa
values do not sum to unity. Thus, the
remaining is regarded as ignorance, which is
p
1
(C
1
, C
2
, C
3
, C
4
)
=
0.20 and
p
2
(C
1
, C
2
, C
3
, C
4
)
0.50. By assigning the
bpa
to different elements, e.g.
p
1
(C
1
) and
p
1
(C
1
, C
2
, C
3
), indeed can refl ect the decision maker's uncertainty
in the damage classifi cation. Using the DST rule of combination (Equation
6.6), the information from the DMs are aggregated and summarized below
and in Table 6.1.
Thus, the fi nal DST results are:
p
(C
1
)
=
=
0.25;
p
(C
2
)
=
0.23;
p
(C
2
, C
3
)
=
0.15;
p
(C
1
, C
2
, C
3
)
=
0.25; and
p
(C
1
, C
2
, C
3
, C
4
)
=
0.13.
Table 6.1
DS rule of combination for two decision makers
{C1,
C2,
C3,
C4}
{C1,
C2,
C3}
{C1,
C2,
C4}
{C1,
C3,
C4}
{C2,
C3,
C4}
{C1,
C2}
{C1,
C3}
{C1,
C4}
{C2,
C3}
{C2,
C4}
{C3,
C4}
{C1}
{C2}
{C3}
{C4}
DM1
0.40
0
0
0
0
0
0
0
0
0
0.40
0
0
0
0.20
DM1
0
0.30
0
0
0
0
0
0.20
0
0
0
0
0
0
0.50
DST
0.25
0.23
0
0
0
0
0
0.15
0
0
0.25
0
0
0
0.13
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