1. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 1 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Using of Fuzzy Set Theory to address the uncertainty of susceptibility to drought Contents: 1Introduction 2How does Fuzzy Set Theory work? 3The use of Fuzzy Set Theory in the Security Diagrams project 4Conclusions Contents  Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

2. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 2 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 1Introduction  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

3. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 3 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Imprecise knowledge about the effect of indicators Non-linear relationships Complex structure of influence factors  Difficult to develop exact models of vulnerability Principle difficulties in vulnerability research  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

4. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 4 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 … offers a possibility to use imprecise categories … can handle complex relationships in relatively easy rule systems … enables linguistic modelling, but with quantitative results Fuzzy Set Theory  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

5. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 5 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 2How does Fuzzy Set Theory work?  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

6. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 6 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 A simple model of susceptibility Income poor  rich Conflicts instable  stable Suscept- ibility very low  high Rule system (Inference): 1If people are poor and political situation is stable then susceptibility is medium to low. 2If people are poor and situation is instable then susceptibility is high. 3If people are rich and situation is instable then susceptibility is medium to high. 4If people are rich and situation is stable then susceptibility is very low. +  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

7. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 7 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Yearly income [US$] 1001.00010.000100.0001.000.000 poorrich sharp threshold Binary Logic  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

8. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 8 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Yearly income [US$] poorrich no sharp threshold 1001.00010.000100.0001.000.000 0 1 0,5 Fuzzy Logic degree of member- ship 5.000 0,3 0,7  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

9. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 9 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 GDP per capita [US$] poorrich 1001.00010. 000100.0001.000.000 0 1 0,5 Conflict involvement [1 = no conflict; 2 = latent conflict; 3 = non-violent conflicts; 4 = violent crisis; 5 = war] stableinstable 1234 0 1 0,5 Income Conflicts 5 Fuzzification of input variables Rule system (Inference): 1If people are poor and situation is stable then susceptibility is medium to low. 2If people are poor and situation is instable then susceptibility is high. 3If people are rich and situation is instable then susceptibility is medium to high. 4If people are rich and situation is stable then susceptibility is very low. Inference system  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

10. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 10 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 GDP per capita [US$] poorrich 1001.00010. 000100.0001.000.000 0 1 0,5 Conflict involvement [1 = no conflict; 2 = latent conflict; 3 = non-violent conflicts; 4 = violent crisis; 5 = war] stableunstable 1234 0 1 0,5 Income Conflicts Rule system (Inference): 1If people are poor and situation is instable then susceptibility is high. high = Min {0,7; 0,1} = 0,1 2If people are poor and situation is stable then susceptibility is medium to low. medium to low = Min {0,7; 0,9} = 0,7 3If people are rich and situation is instable then susceptibility is medium to high. medium to high = Min {0,3; 0,1} = 0,1 4If people are rich and situation is stable then susceptibility is very low. very low = Min {0,3; 0,9} = 0,3 5 5.000 0,3 0,7 0,9 0,1 Fuzzification of input variablesInference system  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

11. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 11 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Rule system (Inference): 1If people are poor and situation is instable then susceptibility is high. high = Min {0,7; 0,1} = 0,1 2If people are poor and situation is stable then susceptibility is medium to low. medium to low = Min {0,7; 0,9} = 0,7 3If people are rich and situation is instable then susceptibility is medium to high. medium to high = Min {0,3; 0,1} = 0,1 4If people are rich and situation is stable then susceptibility is very low. very low = Min {0,3; 0,9} = 0,3 very low high 00,51 0 1 Susceptibility medium to low medium to high + 0,35 Result:Susceptibility = 0,35 or “medium to low” Center of gravity Inference systemDefuzzification of output variable  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

12. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 12 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 2The 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. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 13 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Applying Fuzzy Set Theory …in a harmonized way by all disciplinary perspectives …in order to get comparable results …for susceptibility and the principle influence factors, …and to easily understand the theoretical models of the other disciplines  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

14. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 14 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Fuzzy System with Subsystems (Psychological Perspective)  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

15. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 15 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 4Conclusions  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

16. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 16 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Disadvantages of Fuzzy Set Theory Based on theory and not explorative,  validation necessary Subjectivity  justification of each step necessary Complexity when using many variables  procedure in sub-systems necessary  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

17. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 17 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Theory based procedure Good integration of expert knowledge Possibility to work with linguistic rule system No subjective thresholds Advantages of Fuzzy Set Theory  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

18. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 18 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Conclusion  Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions

19. Frank Eierdanz (Center for Environmental Systems Research, Kassel, Germany  eierdanz@usf.uni-kassel.de)Slide 19 Security Diagrams Improving a New Approach to Assessing the Risk of Extreme Climate Events on Society 2003 Open Meeting Montréal, Canada 18 Nov. 2003 Thank you very much! Questions?  The end Contents Intro- duction How works Fuzzy Set Theory? Use in the Security Diagrams Project Conclu- sions