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. PRESENTATION SCHEDULE
•
•
•
•
•
Introduction
Study area
Input data
Methods
Results
www.geoinformatics.upol.cz

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. 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. FORMER INSPIRATION
What if…
www.geoinformatics.upol.cz

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. 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. 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. METHODS
www.geoinformatics.upol.cz

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. 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. 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. METHODS – fuzzy set „AND“ operation
Intersect implication of two input variables into output space
www.geoinformatics.upol.cz

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. METHODS – step by step
sw: GNU Octave 3.2.4 and Fuzzy Logic Toolkit 0.2.4
www.geoinformatics.upol.cz
(4)

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. METHODS – fuzzy inference
system
Mamdani FIS principle
www.geoinformatics.upol.cz

18. METHODS – defuzzification
Center of gravity method
www.geoinformatics.upol.cz

19. METHODS – repetition
www.geoinformatics.upol.cz

20. Results
www.geoinformatics.upol.cz

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. RESULTS
www.geoinformatics.upol.cz

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