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

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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

1Introduction

Contents

Intro-duction

How works Fuzzy Set Theory?

Use in the Security Diagrams Project

Conclu-sions

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

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

2How does Fuzzy Set Theory work?

Contents

Intro-duction

How works Fuzzy Set Theory?

Use in the Security Diagrams Project

Conclu-sions

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

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$]

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$]

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

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]

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

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

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

Fuzzy System with Subsystems (Psychological Perspective)

Contents

Intro-duction

How works Fuzzy Set Theory?

Use in the Security Diagrams Project

Conclu-sions

4Conclusions

Contents

Intro-duction

How works Fuzzy Set Theory?

Use in the Security Diagrams Project

Conclu-sions

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

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

Conclusion

Contents

Intro-duction

How works Fuzzy Set Theory?

Use in the Security Diagrams Project

Conclu-sions

Thank you very much!

Questions?

Contents

Intro-duction

How works Fuzzy Set Theory?

Use in the Security Diagrams Project

Conclu-sions

The end