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