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]
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
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,
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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
Peri-urban area
Urbancore
Urban area
Rural area
Ruralcore
Municipality
Urban planners
An area with its own intrinsic
organic rules
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,
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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
Techniques of spatial statisticTechniques of spatial statistic
Bailey and Gatrell classification (1995)
Point Pattern Analysis
Spatially Continuous Analysis
Area Data Analysis
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,
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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
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”
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,
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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
Density functionDensity function Point Pattern AnalysisPoint Pattern Analysis
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,
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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
kernel densitykernel density
)A ..,,A ,A ,y ,(xL n21iii
ττ
1(L)λn
1i2
iLLk
Point Pattern AnalysisPoint Pattern Analysis
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,
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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
Relation between the Relation between the bandwidth dimension bandwidth dimension and the study areaand the study area
ττ
1(L)λn
1i2
iLLk
Point Pattern AnalysisPoint Pattern Analysis
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,
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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
nd
dn
i i 1 minmin
)S(
Nearest neighbor distancePoint Pattern AnalysisPoint Pattern Analysis
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,
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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
Rough set Rough set An Ontology of Uncertainty in Spatial An Ontology of Uncertainty in Spatial
informationinformation
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,
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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
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)
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,
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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
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
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,
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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
)( 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
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,
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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
BoundaryA
InteriorA
ExteriorA
Egenhofer M. J. and Herring J. 1991
Rough setRough set
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,
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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
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
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,
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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
(Wang et al, 2002)
Rough setRough set
Positive region Pos(X)= LXNegative region Neg(X) = U – UXBoundary region Bnd(X) =UX – LX
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,
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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
Case StudyCase Study
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,
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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
Case StudyCase Study
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,
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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
Case StudyCase Study
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,
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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
1 < d <5 (ab/h)
Case StudyCase Study
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,
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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
Case StudyCase Study
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,
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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
Case StudyCase Study
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,
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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
Case StudyCase Study
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,
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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
Case StudyCase Study
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,
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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
Case StudyCase Study
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,
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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
Case StudyCase Study
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,
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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
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
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,
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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
Compactness rateCompactness rate
shape index
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,
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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
Compactness rateCompactness rate
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,
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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
Perimeter RealArea Realcontiguity Real
Perimeter Ideal Area Realcontiguity Ideal
Case StudyCase Study
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,
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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
Changes in area/perimeter ratioChanges in area/perimeter ratio
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,
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Case StudyCase Study
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,
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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
>35%>35%
RR33, R, R44
Case StudyCase Study
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,
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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
<150m
Case StudyCase Study
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,
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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
Case StudyCase Study
PignolaPignola
Real contiguityReal contiguity Ideal Ideal contiguitycontiguity Without Without contiguitycontiguity<< <<
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,
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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
Case StudyCase StudyReal contiguityReal contiguity << Ideal contiguityIdeal contiguity << Without contiguityWithout contiguity
LauriaLauriaAviglianoAvigliano
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,
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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
Case StudyCase StudyWithout contiguityWithout contiguity << Real contiguityReal contiguity << Ideal contiguityIdeal contiguity
PotenzaPotenza
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,
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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
Case StudyCase Study
PotenzaPotenza
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,
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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
Case StudyCase Study
PotenzaPotenza
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,
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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
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,
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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
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
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,
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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
Case StudyCase Study
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
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,
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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
Case StudyCase Study
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,
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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
Case StudyCase Study
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
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,
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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
Case StudyCase Study
LauriaLauria Without contiguityWithout contiguity
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,
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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
Case StudyCase Study
LauriaLauriaReal contiguity Real contiguity << Ideal contiguityIdeal contiguity
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,
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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
Case StudyCase Study
PicernoPicernoWithout contiguityWithout contiguity
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,
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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
Case StudyCase Study
PicernoPicerno
Real contiguity Real contiguity << Ideal contiguityIdeal contiguity