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International Cartographic Association (ICA) workshop 8 July 2006, Vienna, Austria International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria The use of Rough Set in Geographical Information Systems Beniamino Murgante, Giuseppe Las Casas, Anna Sansone Dipartimento di Architettura, Pianificazione ed Infrastrutture di Trasporto, Università degli Studi della Basilicata,

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Introduction Economists Increase of costs Increase of real estate economic value Ecologists Loss environmental value Agronomists Agricultural loss of productivity

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Introduction Peri- urban area Urban core Urban area Rural area Rural core Municipality Urban planners An area with its own intrinsic organic rules

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Techniques of spatial statistic Bailey and Gatrell classification (1995) Point Pattern Analysis Spatially Continuous Analysis Area Data Analysis

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems 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”

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Density function Point Pattern Analysis

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems kernel density Point Pattern Analysis

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Relation between the bandwidth dimension and the study area Point Pattern Analysis

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Nearest neighbor distance Point Pattern Analysis

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Rough set An Ontology of Uncertainty in Spatial information

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Information System Rough set Decision System oLet U be a nonempty finite set of objects called the universe oLet 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)

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Indiscernibility Rough set INDISCERNIBILITY RELATION oLet R be an equivalence relation on U, called an INDISCERNIBILITY RELATION EQUIVALENCE CLASS oFor any element x of U, the EQUIVALENCE CLASS of R containing x will be denoted by [ x ] R ELEMENTARY SETS oEquivalence classes of R [ x ] R are called ELEMENTARY SETS in A

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Rough set oIf BX = then the set X is Crisp oIf BX ≠ then the set X is Rough

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Egenhofer M. J. and Herring J Rough set

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Clementini E. and Di Felice P broad boundary ∆A ∆A = A2 − A1 Disjoint and meet Rough set

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems (Wang et al, 2002) Rough set Positive region Pos(X)= LX Negative region Neg(X) = U – UX Boundary region Bnd(X) =UX – LX

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems 1 < d <5 (ab/h) Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Compactness rate Index valueNumber of Centres Good compactness1-1,612 Medium compactness1,61-2,468 Poor compactness2,41-4,8120

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Compactness rate shape index

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Compactness rate

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Changes in area/perimeter ratio

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems >35% R 3, R 4 Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems <150m Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Pignola Real contiguity Ideal contiguity Without contiguity < <

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Real contiguity

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Without contiguity

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Potenza

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Potenza

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Attributes and decision variable Values B= Nature 2000 sites0 Nature 2000 sites, 1 different from Nature 2000 sites Fi= Hydrography 1 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 zones0 classes R3 ed R4, 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% 3 if the slope is bigger than 35% D= Density 1 if the density is less than 1 flats per hectare 2 if the density is included between 1 and 5 flats per hectare 3 if the density is bigger than 5 flats per hectare V= Road Network 1 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 Contiguity0, 1 C2= Ideal Contiguity0, 1 Nei= Nearest neighbor distance (Decision Variable) 1 if the minumum distance is less than 100m 2 if the minumum distance is included between 100 and 200m 3 if the minumum distance is bigger than 200m

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Rough classification Attributes and decision variable Values B= Nature 2000 sites1 different from Nature 2000 sites Fi= Hydrography 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 zones1 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= Density2 if the density is included between 1 and 5 inhabitants per hectare; V= Road Network1 if the distance is less than 200 m.; C1= Real Contiguity1 C2= Ideal Contiguity1 Nei= Nearest neighbor distance (Decision Variable) 1 if the minumum distance less than 100m 2 if the minumum distance included between 100 and 200m

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Map Algebra Rough set LowerUpperAccuracy Without Contiguity ,84% Real Contiguity ,67% Ideal Contiguity ,44% Number of cells

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Lauria Without contiguity

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Lauria Real contiguity

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Picerno Without contiguity

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International Cartographic Association (ICA) workshop on Geospatial Analysis and Modeling - 8 July 2006, Vienna, Austria B.Murgante, G. Las Casas, A.Sansone - The use of Rough Set in Geografical Information Systems Case Study Picerno Real contiguity

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