RURAL AND URBAN AREAS DELIMITATION
USING FUZZY INFERENCE SYSTEM
Vít PÁSZTO

vit.paszto@gmail.com
Alžběta BRYCHTOVÁ, Jiří S...
PRESENTATION SCHEDULE
•
•
•
•
•

Introduction
Study area
Input data
Methods
Results

www.geoinformatics.upol.cz
INTRODUCTION
• Substantial change in population movement
• Together with new settlement, its infrastructure and
other soci...
INTRODUCTION
• … there is no uniform definition of such areas, except
OECD one (2,000 inhab. & 150 p./km2)
• Funds respect...
FORMER INSPIRATION

What if…
www.geoinformatics.upol.cz
STUDY AREA
• Entire area of The Czech Republic
• All of LAU 2 (Local Administrative Unit) units
were processed
• One LAU 2...
INPUT DATA
•
•

Fuzzy inference system (FIS) needs inputs
These were quantitative statistical data:

–
–
–
–
–
–
–

•

Tot...
METHODS
• In 1965 Lotfi A. Zadeh introduced fuzzy sets
• It allows to smooth abrupt boundary values
(on the contrary to Bo...
METHODS

www.geoinformatics.upol.cz
METHODS – step by step

(1)

• Traditional set operations (intersection, union, complement,
…) in fuzzy logic
• First, inp...
METHODS – step by step

Extended threshold values
(by 10 % of range)

Expert threshold values

Input indicators

Rural

(2...
METHODS – step by step
Input indicators

(3)
Expert
weights

Total population

0.35

Total population per built-up area

0...
METHODS – fuzzy set „AND“ operation

Intersect implication of two input variables into output space
www.geoinformatics.upo...
METHOD – step by step

(4)

• The degree of membership was set for each
municipality for each input indicator
• Base rules...
METHODS – step by step

sw: GNU Octave 3.2.4 and Fuzzy Logic Toolkit 0.2.4
www.geoinformatics.upol.cz

(4)
METHODS – fuzzy inference
system
• Evaluation of base rules is done by fuzzy inference
system
• Mamdami inference system w...
METHODS – fuzzy inference
system

Mamdani FIS principle
www.geoinformatics.upol.cz
METHODS – defuzzification

Center of gravity method
www.geoinformatics.upol.cz
METHODS – repetition

www.geoinformatics.upol.cz
Results

www.geoinformatics.upol.cz
RESTULTS
Area

Degree of membership intervals (for rural areas) *

Number of municipalities

rural

<0.5, 1>

5,565

urban...
RESULTS

www.geoinformatics.upol.cz
RURAL AND URBAN AREAS DELIMITATION
USING FUZZY INFERENCE SYSTEM

Vít PÁSZTO

vit.paszto@gmail.com

Department of Geoinform...
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  • {"5":"_\n_\nAlthough being clear\nSamozrejme to muze byt i multikriterialni analyza, ale fuzzy je lepsi\n","22":"Tady rict komentar k tabulce – opet slovne\n","3":"In last 2 decades\nAffected many rural-like municipalities, especially those surrounding larger cities\nBecoming more urban-like \n","20":"U mapy rict slovne, kde jsou typicke vesnice a u mest, ze dochazi k suburbanizaci \n","4":"_\n_\nAlthough being clear\nSamozrejme to muze byt i multikriterialni analyza, ale fuzzy je lepsi\n","21":"Tady rict komentar k tabulce – opet slovne\n"}
  • Vít Pászto - Rural and urban areas delimitation using fuzzy inference system

    1. 1. RURAL AND URBAN AREAS DELIMITATION USING FUZZY INFERENCE SYSTEM Vít PÁSZTO vit.paszto@gmail.com Alžběta BRYCHTOVÁ, Jiří SEDONÍK, Lukáš MAREK, Lenka KUPROVÁ, Pavel TUČEK, Vít VOŽENÍLEK Department of Geoinformatics, Faculty of Science, Palacký University in Olomouc, Czech Republic www.geoinformatics.upol.cz
    2. 2. PRESENTATION SCHEDULE • • • • • Introduction Study area Input data Methods Results www.geoinformatics.upol.cz
    3. 3. INTRODUCTION • Substantial change in population movement • Together with new settlement, its infrastructure and other socioeconomic changes = suburbanization • Less obvious distinction between rural and urban areas • Proper delimitation is needed due to financial support to maintain sustainabality and quality of live in rural-like municipalities • But… www.geoinformatics.upol.cz
    4. 4. INTRODUCTION • … there is no uniform definition of such areas, except OECD one (2,000 inhab. & 150 p./km2) • Funds respects only one rule: – 2,000 inhabitants • This sharp limit is no more suitable • Fuzzy approach brings more realistic results and allows: – to combine more socioeconomic indicators – to define transitional municipalities – respect dynamics of suburbanization www.geoinformatics.upol.cz
    5. 5. FORMER INSPIRATION What if… www.geoinformatics.upol.cz
    6. 6. STUDY AREA • Entire area of The Czech Republic • All of LAU 2 (Local Administrative Unit) units were processed • One LAU 2 unit represents one municipality • There are 6.249 municipalities in Czech Rep. www.geoinformatics.upol.cz
    7. 7. INPUT DATA • • Fuzzy inference system (FIS) needs inputs These were quantitative statistical data: – – – – – – – • Total population Total population per built-up area Flats in family houses per total number of permanently occupied flats Number of completed flats per 1,000 people Population change Driving distance to the county seat Urbanized areas per overall municipality area Time range is from 1993 to 2010 www.geoinformatics.upol.cz
    8. 8. METHODS • In 1965 Lotfi A. Zadeh introduced fuzzy sets • It allows to smooth abrupt boundary values (on the contrary to Boolean logic) • It sets degree of membership for every municipality in range from 0 to 1 • Fuzzy set operations, fuzzy regulation, fuzzy base rules and weights were applied • Closer to human-expert way of evaluation www.geoinformatics.upol.cz
    9. 9. METHODS www.geoinformatics.upol.cz
    10. 10. METHODS – step by step (1) • Traditional set operations (intersection, union, complement, …) in fuzzy logic • First, input numerical (crisp) values were transformed into fuzzy numbers in <0,1> (fuzzification process) • Transformation was done using trapezoidal membership function (left part) within fuzzy inference system (FIS) • Combination of input fuzzy numbers was done by intersection operation „AND“ www.geoinformatics.upol.cz
    11. 11. METHODS – step by step Extended threshold values (by 10 % of range) Expert threshold values Input indicators Rural (2) Urban Rural Urban Total population 1,500 3,500 1,300 3,700 Total population per builtup area 3,500 6,500 3,200 6,800 Flats in family houses per total number of permanently occupied flats 90 70 92 68 Number of completed flats per 1,000 people 10 50 6 54 Population change -2.3 10 -3.53 11.23 Driving distance to the county seat 1,000 -5,000 1,600 5,600 4 0.7 4.3 Urbanized areas per overall 1 municipality area www.geoinformatics.upol.cz
    12. 12. METHODS – step by step Input indicators (3) Expert weights Total population 0.35 Total population per built-up area 0.20 Flats in family houses per total number of permanently occupied flats 0.10 Number of completed flats per 1,000 people 0.10 Population change 0.05 Driving distance to the county seat 0.10 Urbanized areas per overall municipality area 0.10 www.geoinformatics.upol.cz
    13. 13. METHODS – fuzzy set „AND“ operation Intersect implication of two input variables into output space www.geoinformatics.upol.cz
    14. 14. METHOD – step by step (4) • The degree of membership was set for each municipality for each input indicator • Base rules are applied to compute overall degree of membership for particular municipality (combination of input indicators) • Rule base contains 254 rules with weigths www.geoinformatics.upol.cz
    15. 15. METHODS – step by step sw: GNU Octave 3.2.4 and Fuzzy Logic Toolkit 0.2.4 www.geoinformatics.upol.cz (4)
    16. 16. METHODS – fuzzy inference system • Evaluation of base rules is done by fuzzy inference system • Mamdami inference system was used • Inference algorithm allows to fuzzify inputs, to apply base rules and to define fuzzy output set • Fuzzy output set is converted back to crisp value (defuzzification process) • There is need to use proper defuzzification method www.geoinformatics.upol.cz
    17. 17. METHODS – fuzzy inference system Mamdani FIS principle www.geoinformatics.upol.cz
    18. 18. METHODS – defuzzification Center of gravity method www.geoinformatics.upol.cz
    19. 19. METHODS – repetition www.geoinformatics.upol.cz
    20. 20. Results www.geoinformatics.upol.cz
    21. 21. RESTULTS Area Degree of membership intervals (for rural areas) * Number of municipalities rural <0.5, 1> 5,565 urban <0, 0.5) 683 rural <0.66, 1> 4,513 transitional (0.33, 0.66) 1,315 urban <0, 0.33> 420 rural <0.9, 1> 1,208 transitional (0.1, 0.9) 5,008 urban <0, 0.1> 32 rural <1> 37 transitional <0.5> 26 urban <0> 2 Summary of computed results in four membership levels www.geoinformatics.upol.cz
    22. 22. RESULTS www.geoinformatics.upol.cz
    23. 23. RURAL AND URBAN AREAS DELIMITATION USING FUZZY INFERENCE SYSTEM Vít PÁSZTO vit.paszto@gmail.com Department of Geoinformatics, Faculty of Science, Palacký University in Olomouc, Czech Republic www.geoinformatics.upol.cz

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