Justyna Pastwa - Flood vulnerability estimation using FHA geometric mean method

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This document describes a study evaluating flood vulnerability in Lower Silesian Voivodeship, Poland using fuzzy arithmetic operations. It discusses vulnerability factors, available data on past flood events from 2007-2011, and a methodology using fuzzy numbers to estimate attribute weights and rank alternatives based on satisfiability of criteria. Experts provided assessments of criteria importance, which were aggregated into weights. Real data on flood events was then described and the methodology was applied to rank communities by vulnerability.

Education Technology

Evaluation of ﬂood vulnerability in Lower Silesian
Voivodeship using fuzzy arithmetic operations
Justyna Pastwa
Palacky University
pastwa.justyna@gmail.com

October 15, 2013

Justyna Pastwa (UPOL)

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Overview

1

Vulnerability

2

Data

3

Methodology
Theory
Estimation of weights

Justyna Pastwa (UPOL)

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Vulnerability

Justyna Pastwa (UPOL)

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Vulnerability

Justyna Pastwa (UPOL)

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Vulnerability

Justyna Pastwa (UPOL)

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Data

which data are suitable?
which variables are meaningful?
are they available?

Justyna Pastwa (UPOL)

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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 damage
and frequency of events

Justyna Pastwa (UPOL)

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Problems:

imprecise

Justyna Pastwa (UPOL)

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Problems:

imprecise
conﬂicting attributes

Justyna Pastwa (UPOL)

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Problems:

imprecise
conﬂicting attributes
diﬀerent importance

Justyna Pastwa (UPOL)

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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 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.

Justyna Pastwa (UPOL)

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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

Justyna Pastwa (UPOL)

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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
˜


Justyna Pastwa (UPOL)

Short title

...
...
...
..
.

Cn
p˜
1n
p˜
2n
.
.
.

...

pmn
˜







(2)

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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.

Justyna Pastwa (UPOL)

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October 15, 2013

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Weights estimation of the attributes

E1
freq
5
 7
mag 
inj  0

W =
dead  0

eva  4
loss
5


Justyna Pastwa (UPOL)

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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Weights

Justyna Pastwa (UPOL)

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October 15, 2013

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Real data description

Justyna Pastwa (UPOL)

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Real data description

Justyna Pastwa (UPOL)

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Real data description

Justyna Pastwa (UPOL)

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Real data description

Justyna Pastwa (UPOL)

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The End

Justyna Pastwa (UPOL)

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Justyna Pastwa - Flood vulnerability estimation using FHA geometric mean method

1. Evaluation of ﬂood vulnerability in Lower Silesian Voivodeship using fuzzy arithmetic operations Justyna Pastwa Palacky University pastwa.justyna@gmail.com October 15, 2013 Justyna Pastwa (UPOL) Short title October 15, 2013 1 / 18

2. Overview 1 Vulnerability 2 Data 3 Methodology Theory Estimation of weights Justyna Pastwa (UPOL) Short title October 15, 2013 2 / 18

3. Vulnerability Justyna Pastwa (UPOL) Short title October 15, 2013 3 / 18

4. Vulnerability Justyna Pastwa (UPOL) Short title October 15, 2013 4 / 18

5. Vulnerability Justyna Pastwa (UPOL) Short title October 15, 2013 5 / 18

6. Data which data are suitable? which variables are meaningful? are they available? Justyna Pastwa (UPOL) Short title October 15, 2013 6 / 18

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 Justyna Pastwa (UPOL) Short title October 15, 2013 6 / 18

8. Problems: imprecise Justyna Pastwa (UPOL) Short title October 15, 2013 7 / 18

9. Problems: imprecise conﬂicting attributes Justyna Pastwa (UPOL) Short title October 15, 2013 7 / 18

10. Problems: imprecise conﬂicting attributes diﬀerent importance Justyna Pastwa (UPOL) Short title October 15, 2013 7 / 18

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. Justyna Pastwa (UPOL) Short title October 15, 2013 8 / 18

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 Justyna Pastwa (UPOL) Short title October 15, 2013 9 / 18

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 ˜  Justyna Pastwa (UPOL) Short title ... ... ... .. . Cn p˜ 1n p˜ 2n . . . ... pmn ˜      (2) October 15, 2013 10 / 18

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. Justyna Pastwa (UPOL) Short title October 15, 2013 11 / 18

15. Weights estimation of the attributes E1 freq 5  7 mag  inj  0  W = dead  0  eva  4 loss 5  Justyna Pastwa (UPOL) 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         October 15, 2013 (4) 12 / 18

16. Weights Justyna Pastwa (UPOL) Short title October 15, 2013 13 / 18

17. Real data description Justyna Pastwa (UPOL) Short title October 15, 2013 14 / 18

18. Real data description Justyna Pastwa (UPOL) Short title October 15, 2013 15 / 18

19. Real data description Justyna Pastwa (UPOL) Short title October 15, 2013 16 / 18

20. Real data description Justyna Pastwa (UPOL) Short title October 15, 2013 17 / 18

21. The End Justyna Pastwa (UPOL) Short title October 15, 2013 18 / 18

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Justyna Pastwa - Flood vulnerability estimation using FHA geometric mean method