vít pászto- rural and urban areas delimitation using fuzzy inference system

www.geoinformatics.upol.cz

RURAL AND URBAN AREAS DELIMITATION USING FUZZY INFERENCE SYSTEM

Vít PÁ[email protected]

Alžběta BRYCHTOVÁ, Jiří SEDONÍK, Lukáš MAREK, Lenka KUPROVÁ, Pavel TUČEK,Vít VOŽENÍLEK

Department of Geoinformatics, Faculty of Science, Palacký University in Olomouc, Czech Republic


PRESENTATION SCHEDULE

• Introduction• Study area• Input data• Methods• Results


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…


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


FORMER INSPIRATION

What if…


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.


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


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


METHODS


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“



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



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


METHODS – fuzzy set „AND“ operation

Intersect implication of two input variables into output space


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



sw: GNU Octave 3.2.4 and Fuzzy Logic Toolkit 0.2.4


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


METHODS – fuzzy inference system

Mamdani FIS principle


METHODS – defuzzification

Center of gravity method


METHODS – repetition


Results


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


RESULTS


RURAL AND URBAN AREAS DELIMITATION USING FUZZY INFERENCE SYSTEM

Vít PÁ[email protected]

Department of Geoinformatics, Faculty of Science, Palacký University in Olomouc, Czech Republic

vít pászto- rural and urban areas delimitation using fuzzy inference system

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