Justyna Pastwa - Flood vulnerability estimation using FHA geometric mean method

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Justyna Pastwa - Flood vulnerability estimation using FHA geometric mean method

  1. 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. 2. Overview 1 Vulnerability 2 Data 3 Methodology Theory Estimation of weights Justyna Pastwa (UPOL) Short title October 15, 2013 2 / 18
  3. 3. Vulnerability Justyna Pastwa (UPOL) Short title October 15, 2013 3 / 18
  4. 4. Vulnerability Justyna Pastwa (UPOL) Short title October 15, 2013 4 / 18
  5. 5. Vulnerability Justyna Pastwa (UPOL) Short title October 15, 2013 5 / 18
  6. 6. Data which data are suitable? which variables are meaningful? are they available? Justyna Pastwa (UPOL) Short title October 15, 2013 6 / 18
  7. 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. 8. Problems: imprecise Justyna Pastwa (UPOL) Short title October 15, 2013 7 / 18
  9. 9. Problems: imprecise conflicting attributes Justyna Pastwa (UPOL) Short title October 15, 2013 7 / 18
  10. 10. Problems: imprecise conflicting attributes different importance Justyna Pastwa (UPOL) Short title October 15, 2013 7 / 18
  11. 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. 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. 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. 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. 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. 16. Weights Justyna Pastwa (UPOL) Short title October 15, 2013 13 / 18
  17. 17. Real data description Justyna Pastwa (UPOL) Short title October 15, 2013 14 / 18
  18. 18. Real data description Justyna Pastwa (UPOL) Short title October 15, 2013 15 / 18
  19. 19. Real data description Justyna Pastwa (UPOL) Short title October 15, 2013 16 / 18
  20. 20. Real data description Justyna Pastwa (UPOL) Short title October 15, 2013 17 / 18
  21. 21. The End Justyna Pastwa (UPOL) Short title October 15, 2013 18 / 18

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