The use of Rough Set in Geographical Information Systems

International Cartographic Association (ICA) workshopInternational Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, 8 July 2006, Vienna, AustriaAustriaThe use of Rough Set in The use of Rough Set in

Geographical Geographical Information SystemsInformation Systems

Beniamino Murgante, Giuseppe Las Casas, Anna Sansone

Dipartimento di Architettura, Pianificazione ed Infrastrutture di Trasporto, Università degli Studi della Basilicata, [email protected], [email protected], [email protected]

mailto:[email protected]



International Cartographic Association (ICA) workshop on International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Geospatial Analysis and Modeling - 8 July 2006, Vienna,

AustriaAustria

B.Murgante, G. Las Casas, A.Sansone - B.Murgante, G. Las Casas, A.Sansone - The use of The use of Rough Set in Geografical Information SystemsRough Set in Geografical Information Systems

IntroductionIntroduction

Economists

Increase of costs

Increase of real estate economic

value

EcologistsLoss

environmental value

Agronomists

Agricultural loss of

productivity


AustriaAustria


IntroductionIntroduction

Peri-urban area

Urbancore

Urban area

Rural area

Ruralcore

Municipality

Urban planners

An area with its own intrinsic

organic rules


AustriaAustria


Techniques of spatial statisticTechniques of spatial statistic

Bailey and Gatrell classification (1995)

Point Pattern Analysis

Spatially Continuous Analysis

Area Data Analysis


AustriaAustria


Point Pattern AnalysisPoint Pattern Analysis

Point Pattern Analysis

First order effects(Absolute location)

Second order effects

(Relative location)

Tobler's First Law of Geography “All things are related, but nearby things are more related than distant things”


AustriaAustria


Density functionDensity function Point Pattern AnalysisPoint Pattern Analysis


AustriaAustria


kernel densitykernel density

)A ..,,A ,A ,y ,(xL n21iii

ττ

1(L)λn

1i2

iLLk



AustriaAustria


Relation between the Relation between the bandwidth dimension bandwidth dimension and the study areaand the study area

ττ

1(L)λn

1i2

iLLk



AustriaAustria


nd

dn

i i 1 minmin

)S(

Nearest neighbor distancePoint Pattern AnalysisPoint Pattern Analysis


AustriaAustria


Rough set Rough set An Ontology of Uncertainty in Spatial An Ontology of Uncertainty in Spatial

informationinformation


AustriaAustria


Information System Information System

A) (U, IS

Attributes lConditiona d-A attributesother a

Rough set Rough set

set value V A a a

Decision SystemDecision System

Ad )A (U, DS d

o Let U be a nonempty finite set of objects called the universe

o Let A be a nonempty finite set of attributes

A decision system is an information system in which the values of a special decision attribute classify the cases d≠A (decision attribute)


AustriaAustria


IndiscernibilityIndiscernibility (B) Ind AB

Bb )b()b( (B) Ind are e jiji xxxx

Rough set Rough set

o Let R be an equivalence relation on U, called an INDISCERNIBILITY RELATIONINDISCERNIBILITY RELATION

o For any element x of U, the EQUIVALENCE CLASSEQUIVALENCE CLASS of R containing x will be denoted by [ x ] R

o Equivalence classes of R [ x ] R are called ELEMENTARY SETSELEMENTARY SETS in A


AustriaAustria


)( XxUxLX Bindii

LXUXBX

)(/)()( Accuracy UXcardLXcardXB

)( XxUxUX Bindii

Rough setRough set

o If BX = then the set X is Crisp o If BX ≠ then the set X is Rough


AustriaAustria


BoundaryA

InteriorA

ExteriorA

Egenhofer M. J. and Herring J. 1991

Rough setRough set


AustriaAustria


Clementini E. and Di Felice P. 1996

A2 and A1 21 AA

boundaryinner 1 Aboundary outer 2 A

broad boundary ∆A

∆A = A2 − A1Interior A- A A 2

ExteriorA 2

2 A -R

Disjoint and meet

Rough setRough set


AustriaAustria


(Wang et al, 2002)

Rough setRough set

Positive region Pos(X)= LXNegative region Neg(X) = U – UXBoundary region Bnd(X) =UX – LX


AustriaAustria


Case StudyCase Study


AustriaAustria


1 < d <5 (ab/h)



AustriaAustria




AustriaAustria


Compactness rateCompactness rate

1Perimeter IdealPerimeter Real

Index value Number of CentresGood compactness 1-1,6 12Medium compactness 1,61-2,4 68

Poor compactness 2,41-4,81 20


AustriaAustria



shape index


AustriaAustria




AustriaAustria


Perimeter RealArea Realcontiguity Real

Perimeter Ideal Area Realcontiguity Ideal



AustriaAustria


Changes in area/perimeter ratioChanges in area/perimeter ratio


AustriaAustria




AustriaAustria


>35%>35%

RR33, R, R44



AustriaAustria


<150m



AustriaAustria



PignolaPignola

Real contiguityReal contiguity Ideal Ideal contiguitycontiguity Without Without contiguitycontiguity<< <<


AustriaAustria


Case StudyCase StudyReal contiguityReal contiguity << Ideal contiguityIdeal contiguity << Without contiguityWithout contiguity

LauriaLauriaAviglianoAvigliano


AustriaAustria


Case StudyCase StudyWithout contiguityWithout contiguity << Real contiguityReal contiguity << Ideal contiguityIdeal contiguity

PotenzaPotenza


AustriaAustria



PotenzaPotenza


AustriaAustria


Case StudyCase StudyAttributes and decision variable Attributes and decision variable ValuesValues

B= Nature 2000 sites 0 Nature 2000 sites, 1 different from Nature 2000 sites

Fi= Hydrography1 if the distance is less than 150 m.2 if the distance is included between 150 m. and 800 m.3 if the distance is bigger than 800 m.

Fr= Hydro-geological risk zones 0 classes R3 ed R4, 1 different from classes R3 ed R4

P= Slope1 if the slope is less than 23,6%2 if the slope is included between 23,6% and 35%3 if the slope is bigger than 35%

D= Density1 if the density is less than 1 flats per hectare2 if the density is included between 1 and 5 flats per hectare3 if the density is bigger than 5 flats per hectare

V= Road Network1 if the distance is less than 200 m.2 if the distance is included between 200 and 700m.3 if the distance is less than 700 m.

C1= Real Contiguity 0, 1C2= Ideal Contiguity 0, 1

Nei= Nearest neighbor distance (Decision Variable)

1 if the minumum distance is less than 100m2 if the minumum distance is included between 100 and 200m3 if the minumum distance is bigger than 200m


AustriaAustria


Case StudyCase StudyRough classificationRough classification

Attributes and decision Attributes and decision variable variable

ValuesValues

B= Nature 2000 sites 1 different from Nature 2000 sites

Fi= Hydrography2 if the distance is included between 150 m. and 800 m.3 if the distance is bigger than 800 m.

Fr= Hydro-geological risk zones

1 different from classes R3 ed R4

P= Slope 1 if the slope is less than 23,6%2 if the slope is included between 23,6% and 35%

D= Density 2 if the density is included between 1 and 5 inhabitants per hectare;

V= Road Network 1 if the distance is less than 200 m.;C1= Real Contiguity 1C2= Ideal Contiguity 1Nei= Nearest neighbor Nei= Nearest neighbor distance (Decision Variable)distance (Decision Variable)

1 if the minumum distance less than 100m2 if the minumum distance included between 100 and 200m


AustriaAustria



B Fi Fr D P V 1 2 Totale1 2 1 2 1 1 231461 102 2315631 3 1 2 1 1 624127 309 6244361 2 1 2 2 1 20390 203901 3 1 2 2 1 52467 52467

Lw 72857 0Up 928856 855999Acc 7,84%

Nei

B Fi Fr D P V C1 1 2 Totale1 2 1 2 1 1 1 103914 1039141 3 1 2 1 1 1 297750 50 2978001 2 1 2 2 1 1 8946 89461 3 1 2 2 1 1 25196 25196

Lw 138056Up 435856Acc 31,67%

Nei

B Fi Fr D P V C2 1 2 Totale1 2 1 2 1 1 1 121089 32 1211211 3 1 2 1 1 1 358388 139 3585271 2 1 2 2 1 1 12127 121271 3 1 2 2 1 1 32087 32087

Lw 44214Up 523862Acc 8,44%

Nei


AustriaAustria




AustriaAustria



Map Algebra

Rough set

Lower UpperAccuracy

Without Contiguity 1721768 72857 928856 7,84%Real Contiguity 766864 138056 435856 31,67%Ideal Contiguity 1208171 44214 523862 8,44%

Number of cells


AustriaAustria



LauriaLauria Without contiguityWithout contiguity


AustriaAustria



LauriaLauriaReal contiguity Real contiguity << Ideal contiguityIdeal contiguity


AustriaAustria



PicernoPicernoWithout contiguityWithout contiguity


AustriaAustria



PicernoPicerno

Real contiguity Real contiguity << Ideal contiguityIdeal contiguity

The use of Rough Set in Geographical Information Systems

Documents

Transcript of The use of Rough Set in Geographical Information Systems