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www.geoinformatics.upol.cz
RURAL AND URBAN AREAS DELIMITATION USING FUZZY INFERENCE SYSTEM
Vít PÁSZTOvit.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
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PRESENTATION SCHEDULE
• Introduction• Study area• Input data• Methods• Results
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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…
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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
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FORMER INSPIRATION
What if…
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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.
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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
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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
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METHODS
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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“
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METHODS – step by step (2)
Input indicatorsExpert threshold values Extended threshold values
(by 10 % of range)
Rural Urban Rural UrbanTotal population 1,500 3,500 1,300 3,700Total population per built-up 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 11.23Driving distance to the county seat 1,000 -5,000 1,600 5,600
Urbanized areas per overall municipality area 1 4 0.7 4.3
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METHODS – step by step (3)
Input indicators Expert weights
Total population 0.35Total population per built-up area 0.20Flats in family houses per total number of permanently occupied flats 0.10Number of completed flats per 1,000 people 0.10Population change 0.05Driving distance to the county seat 0.10Urbanized areas per overall municipality area 0.10
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METHODS – fuzzy set „AND“ operation
Intersect implication of two input variables into output space
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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
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METHODS – step by step (4)
sw: GNU Octave 3.2.4 and Fuzzy Logic Toolkit 0.2.4
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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
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METHODS – fuzzy inference system
Mamdani FIS principle
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METHODS – defuzzification
Center of gravity method
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METHODS – repetition
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Results
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RESTULTS
Summary of computed results in four membership levels
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
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RESULTS
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RURAL AND URBAN AREAS DELIMITATION USING FUZZY INFERENCE SYSTEM
Vít PÁSZTOvit.paszto@gmail.com
Department of Geoinformatics, Faculty of Science, Palacký University in Olomouc, Czech Republic
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