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xb
−
⎧
β
Dx
() (
=
)
x Mb
∈
[ ,]
⎪
⎪
(3)
Mb
xb
−
⎨
−
⎪
Dx
()
=−
(
)
β
x bd
∈
[, ]
⎪
⎩
db
−
⎧
xb
−
β
μ
() 0.5[1 (
x
=
+
)]
x M b
∈
[ ,]
⎪
⎪
or
(4)
Mb
xb
−
⎨
−
⎪
β
μ
() 0.5[1 (
x
=
−
)]
x
∈
[, ]
b d
⎪
⎩
db
−
Where β is index bigger than 0, usually we take it as β=1, viz. (1) and (3) become linear
functions which equal Equations (2) and (4).
3 VFS for Comprehensive Evaluation of the Flood Degree-Taking
Henan Province for Examples
According to the 41 years' practical series material from 1950 to 1990 in Henan
province([6]), we take disaster area-
xj
as the
disaster degree's indicator and by frequency analysis we classify it into four levels:
small, medium, large and extreme (see Table 1).
xj
(1,
)
(2,
)
and direct economic loss-
Table 1.
Henan flood disaster rating standard
Inundated area (hm
2
)
Disaster level
Direct economic losses
(Billion yuan)
Grade
number
small flood
0~46.7
0~9.5
1
medium flood
46.7~136.7
9.5~31.0
2
large flood
136.7~283.3
31.0~85.0
3
extreme flood
283.3~
85.0~
4
According to Table 1 and Chen ([2]), we set up values matrix of parameters for
calculating difference function of VFS:
[0, 46.7]
[46.7,136.7]
[136.7, 283.3]
[283.3,1000]
⎡
⎤
I
=
⎢
⎥
[,]
ab
[0, 9.5]
[9.5, 31.0]
[31.0, 85]
[85, 300]
⎣
⎦
[0,136.7]
[0, 283.3]
[46.7,1000]
[136.7,1000]
⎡
⎤
I
=
⎦
⎢
⎥
[, ]
cd
[0, 31.0]
[0,85]
[9.5, 300]
[31.0, 300]
⎣
0
76.7
234.4333
1000
⎡
⎤
M
=
⎢
⎥
0
16.6667
67
300
⎣
⎦
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