Using of Fuzzy Set Theory to address the uncertainty of susceptibility to drought

1. Using of Fuzzy Set Theory to address the uncertainty of susceptibility to drought • Contents: • Introduction • How does Fuzzy Set Theory work? • The use of Fuzzy Set Theory in the Security Diagrams project • Conclusions  Contents Intro-duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu-sions

2. 1 Introduction Contents  Intro-duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu-sions

3. Principle difficulties in vulnerability research • Imprecise knowledge about the effect of indicators • Non-linear relationships • Complex structure of influence factors •  Difficult to develop exact models of vulnerability Contents  Intro-duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu-sions

4. Fuzzy Set Theory … offers a possibility to use imprecise categories … can handle complex relationships in relatively easy rule systems … enables linguistic modelling, but with quantitative results Contents  Intro-duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu-sions

5. 2 How does Fuzzy Set Theory work? Contents Intro-duction  How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu-sions

6. Income poor  rich + Conflicts instable  stable A simple model of susceptibility Contents • Rule system (Inference): • If people are poorand political situation is stable then susceptibility is medium to low. • If people are poorand situation is instable then susceptibility is high. • If people are richand situation is instable then susceptibility is medium to high. • If people are richand situation is stable then susceptibility is very low. Intro-duction  How works Fuzzy Set Theory? Suscept-ibility very low  high Use in the Security Diagrams Project Conclu-sions

7. Binary Logic sharp threshold Contents poor rich Intro-duction  How works Fuzzy Set Theory? Use in the Security Diagrams Project 100 1.000 10.000 100.000 1.000.000 Conclu-sions Yearly income [US$]

8. 1 0,7 0,5 0,3 0 100 1.000 10.000 100.000 1.000.000 5.000 Fuzzy Logic no sharp threshold Contents poor rich Intro-duction degree of member-ship  How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu-sions Yearly income [US$]

9. Fuzzification of input variables Income poor rich 1 0,5 0 100 1.000 10. 000 100.000 1.000.000 GDP per capita [US$] Conflicts stable instable 1 0,5 0 1 2 3 4 5 Conflict involvement [1 = no conflict; 2 = latent conflict; 3 = non-violentconflicts; 4 = violent crisis; 5 = war] Inference system • Rule system (Inference): • If people are poorand situation is stable then susceptibility is medium to low. • If people are poorand situation is instable then susceptibility is high. • If people are richand situation is instable then susceptibility is medium to high. • If people are richand situation is stable then susceptibility is very low. Contents Intro-duction  How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu-sions

10. Fuzzification of input variables Inference system Income • Rule system (Inference): • If people are poorand situation isinstable then susceptibility ishigh.high = Min {0,7; 0,1} = 0,1 • If people are poorand situation isstable then susceptibility ismedium to low.medium to low = Min {0,7; 0,9} = 0,7 • If people are richand situation isinstable then susceptibility ismedium to high.medium to high = Min {0,3; 0,1} = 0,1 • If people are richand situation isstable then susceptibility is verylow.very low = Min {0,3; 0,9} = 0,3 poor rich 1 0,7 Contents 0,5 Intro-duction 0,3  0 How works Fuzzy Set Theory? 100 1.000 10. 000 100.000 1.000.000 5.000 GDP per capita [US$] Use in the Security Diagrams Project Conflicts stable unstable 1 0,9 Conclu-sions 0,5 0,1 0 1 2 3 4 5 Conflict involvement [1 = no conflict; 2 = latent conflict; 3 = non-violentconflicts; 4 = violent crisis; 5 = war]

11. Center ofgravity + 0,35 Result: Susceptibility = 0,35 or “medium to low” Inference system Defuzzification of output variable • Rule system (Inference): • If people are poorand situation isinstable then susceptibility ishigh.high = Min {0,7; 0,1} = 0,1 • If people are poorand situation isstable then susceptibility ismedium to low.medium to low = Min {0,7; 0,9} = 0,7 • If people are richand situation isinstable then susceptibility ismedium to high.medium to high = Min {0,3; 0,1} = 0,1 • If people are richand situation isstable then susceptibility is verylow.very low = Min {0,3; 0,9} = 0,3 Contents Susceptibility Intro-duction verylow mediumto low mediumto high high  How works Fuzzy Set Theory? 1 0,5 Use in the Security Diagrams Project 0 0 0,5 1 Conclu-sions

12. 2 The use of Fuzzy Set Theory in the Security Diagrams project Contents Intro-duction How works Fuzzy Set Theory?  Use in the Security Diagrams Project Conclu-sions

13. Applying Fuzzy Set Theory … in a harmonized way by all disciplinary perspectives Contents … in order to get comparable results Intro-duction … for susceptibility and the principle influence factors, How works Fuzzy Set Theory? … and to easily understand the theoretical models of the other disciplines  Use in the Security Diagrams Project Conclu-sions

14. Fuzzy System with Subsystems (Psychological Perspective) Contents Intro-duction How works Fuzzy Set Theory?  Use in the Security Diagrams Project Conclu-sions

15. 4 Conclusions Contents Intro-duction How works Fuzzy Set Theory? Use in the Security Diagrams Project  Conclu-sions

16. Disadvantages of Fuzzy Set Theory • Based on theory and not explorative,  validation necessary Contents Intro-duction • Subjectivity justification of each step necessary How works Fuzzy Set Theory? • Complexity when using many variables procedure in sub-systems necessary Use in the Security Diagrams Project  Conclu-sions

17. Advantages of Fuzzy Set Theory • Theory based procedure Contents • Good integration of expert knowledge Intro-duction • Possibility to work with linguistic rule system How works Fuzzy Set Theory? • No subjective thresholds Use in the Security Diagrams Project  Conclu-sions

18. Conclusion Contents Intro-duction How works Fuzzy Set Theory? Use in the Security Diagrams Project  Conclu-sions

19. Thank you very much! Questions? Contents Intro-duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu-sions  The end