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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

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

… 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

2 How does Fuzzy Set Theory work?

Contents

Intro-duction

How works Fuzzy Set Theory?

Use in the Security Diagrams Project

Conclu-sions

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

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$]

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]

+

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

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

… 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

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

Contents

Intro-duction

How works Fuzzy Set Theory?

Use in the Security Diagrams Project

Conclu-sions

Questions?

Contents

Intro-duction

How works Fuzzy Set Theory?

Use in the Security Diagrams Project

Conclu-sions

The end

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