Evaluation of flood vulnerability in Lower SilesianVoivodeship using fuzzy arithmetic operations
Justyna Pastwa
Palacky University
October 15, 2013
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Overview
1 Vulnerability
2 Data
3 MethodologyTheoryEstimation of weights
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Vulnerability
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Vulnerability
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Vulnerability
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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 damageand frequency of events
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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 damageand frequency of events
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Problems:
imprecise
conflicting attributes
different importance
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Problems:
imprecise
conflicting attributes
different importance
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Problems:
imprecise
conflicting attributes
different importance
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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 helpof information supplied by n experts (Ej ; j = 1, 2, . . . , n) on each of Kcriteria (Ck ; k = 1, 2, . . . ,K ). DM wish to find which from alternativessatisfy criteria the best.
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Methodology – weights estimation
The average of fuzzy numbers across all the experts:
q̃k = (1/n) � ( ˜ck1 ⊕ ˜ck2 ⊕ . . .⊕ ˜ckn) (1)
where � and ⊕ are fuzzy multiplication and addition, respectively
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Methodology – fuzzy rank score matrix
For each criteria, rank the degree of satisfiability for each system withrespect to each criteria item by integer numbers 1, 2, . . . , etc:
A =
C1 C2 . . . Cn
A1 p̃11 p̃12 . . . p̃1nA2 p̃21 p̃22 . . . p̃2n...
......
. . ....
Am ˜pm1 ˜pm2 . . . ˜pmn
(2)
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Methodology – ranking alternatives
Perform following operations:
R = A�W T =
p̃11 � w̃1 ⊕ p̃12 � w̃2 ⊕ . . .⊕ p̃1n � w̃n
p̃21 � w̃1 ⊕ p̃22 � w̃2 ⊕ . . .⊕ p̃2n � w̃n...
˜pm1 � w̃1 ⊕ ˜pm2 � w̃2 ⊕ . . .⊕ ˜pmn � w̃n
=
R(1)R(2)
...R(m)
(3)
Deffuzzification.
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Weights estimation of the attributes
W =
E1 E2 E3 E4 E5 E6 E7 E8 E9 E10
freq 5 7 7 10 0 10 9 1 4 10mag 7 10 5 10 0 10 4 1 2 8inj 0 4 0 0 0 0 0 0 0 0dead 0 4 0 0 0 0 0 0 0 0eva 4 8 1 6 0 0 7 0 2 1loss 5 10 3 8 1 0 9 4 2 5
(4)
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Weights
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Real data description
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Real data description
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Real data description
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Real data description
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The End
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