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Utilizing Fuzzy Set Theory for Uncertainty in Drought Susceptibility Analysis

This paper discusses the application of Fuzzy Set Theory to address uncertainties in drought susceptibility analysis. It covers the basics of Fuzzy Set Theory, its use in the Security Diagrams project, and concludes with the benefits it offers in handling complex relationships. The paper explores the challenges in vulnerability research and showcases a simple model of susceptibility based on income and stability. From sharp binary logic to fuzzy logic without sharp thresholds, the text delves into fuzzification of input variables and inference systems. It demonstrates how Fuzzy Set Theory aids in linguistic modeling while producing quantitative results. The use of Fuzzy Set Theory in security projects is emphasized, highlighting its ability to harmonize various disciplinary perspectives for comprehensive results.

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Utilizing Fuzzy Set Theory for Uncertainty in Drought Susceptibility Analysis

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  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

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