1. Evaluation of flood vulnerability in Lower Silesian
Voivodeship using fuzzy arithmetic operations
Justyna Pastwa
Palacky University
pastwa.justyna@gmail.com
October 15, 2013
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2. Overview
1
Vulnerability
2
Data
3
Methodology
Theory
Estimation of weights
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3. Vulnerability
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4. Vulnerability
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5. Vulnerability
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6. Data
which data are suitable?
which variables are meaningful?
are they available?
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7. Data
which data are suitable?
which variables are meaningful?
are they available?
Used data:
registered events of floods, 2007–2011, Lower Silesian Voivodeship
magnitude, number of injured, fatalities and evacuated, flood damage
and frequency of events
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8. Problems:
imprecise
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9. Problems:
imprecise
conflicting attributes
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10. Problems:
imprecise
conflicting attributes
different importance
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11. Methodology
Lets consider the problem of ranking m alternatives (Ai ; i = 1, 2, . . . , m)
by a decision maker (DM). DM wish to rank m alternatives with the help
of information supplied by n experts (Ej ; j = 1, 2, . . . , n) on each of K
criteria (Ck ; k = 1, 2, . . . , K ). DM wish to find which from alternatives
satisfy criteria the best.
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12. Methodology – weights estimation
The average of fuzzy numbers across all the experts:
qk = (1/n)
˜
where
(c˜ ⊕ c˜ ⊕ . . . ⊕ c˜ )
k1
k2
kn
(1)
and ⊕ are fuzzy multiplication and addition, respectively
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13. Methodology – fuzzy rank score matrix
For each criteria, rank the degree of satisfiability for each system with
respect to each criteria item by integer numbers 1, 2, . . . , etc:
C1
C2
A1
p˜
p˜
11
12
 p˜
A2  21 p˜
22
A= .  .
.
.  .
.
.
.
.
˜
Am pm1 pm2
˜

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...
...
...
..
.
Cn
p˜
1n
p˜
2n
.
.
.
...
pmn
˜





(2)
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14. Methodology – ranking alternatives
Perform following operations:

R = A WT
p˜
11
 p˜
 21
= 

pm1
˜
w1 ⊕ p˜
˜
12
w1 ⊕ p˜
˜
22
w2 ⊕ . . . ⊕ p˜
˜
1n
w2 ⊕ . . . ⊕ p˜
˜
2n
.
.
.
w1 ⊕ pm2
˜
˜
w2 ⊕ . . . ⊕ pmn
˜
˜

wn
˜
wn 
˜ 
=

wn
˜





R(1)
R(2)
.
.
.





R(m)
(3)
Deffuzzification.
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15. Weights estimation of the attributes
E1
freq
5
 7
mag 
inj  0

W =
dead  0

eva  4
loss
5

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E2
7
10
4
4
8
10
E3
7
5
0
0
1
3
E4
10
10
0
0
6
8
E5
0
0
0
0
0
1
Short title
E6
10
10
0
0
0
0
E7
9
4
0
0
7
9
E8
1
1
0
0
0
4
E9
4
2
0
0
2
2
E10
10
8
0
0
1
5








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16. Weights
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17. Real data description
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18. Real data description
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19. Real data description
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20. Real data description
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21. The End
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