The use of Rough Set in Geographical Information Systems

1. The use of Rough Set in Geographical Information Systems Dipartimento di Architettura, Pianificazione ed Infrastrutture di Trasporto, Università degli Studi della Basilicata, murgante@unibas.it, lascasas@unibas.it, asansone@unibas.it Beniamino Murgante, Giuseppe Las Casas, Anna Sansone

2. Introduction Increase of costs Economists Increase of real estate economic value Loss environmental value Ecologists Agricultural loss of productivity Agronomists

3. Municipality Urban area Urban core Rural core Peri-urban area Rural area Introduction Urban planners An area with its own intrinsic organic rules

4. Techniques of spatial statistic Bailey and Gatrell classification (1995) Point Pattern Analysis Spatially Continuous Analysis Area Data Analysis

5. Point Pattern Analysis Tobler's First Law of Geography “All things are related, but nearby things are more related than distant things” Point Pattern Analysis Second order effects (Relative location) First order effects (Absolute location)

6. Point Pattern Analysis Density function

7. Point Pattern Analysis kernel density

8. Point Pattern Analysis Relation between the bandwidth dimension and the study area

9. Point Pattern Analysis Nearest neighbor distance

10. Rough set An Ontology of Uncertainty in Spatial information

11. Rough set Information System • Let U be a nonempty finite set of objects called the universe • Let A be a nonempty finite set of attributes Decision System A decision system is an information system in which the values of a special decision attribute classify the cases d≠A (decision attribute)

12. Rough set Indiscernibility • Let R be an equivalence relation on U, called an INDISCERNIBILITY RELATION • For any element x of U, the EQUIVALENCE CLASS of R containing x will be denoted by [ x ] R • Equivalence classes of R [ x ] R are called ELEMENTARY SETS in A

13. Rough set • If BX =  then the set X is Crisp • If BX ≠ then the set X is Rough

14. Rough set Egenhofer M. J. and Herring J. 1991

15. Rough set broad boundary ∆A ∆A = A2 − A1 Clementini E. and Di Felice P. 1996 Disjoint and meet

16. Rough set Positive region Pos(X)= LX Negative region Neg(X) = U – UX Boundary region Bnd(X) =UX– LX (Wang et al, 2002)

17. Case Study

18. Case Study

19. Case Study

20. Case Study 1 < d <5 (ab/h)

21. Case Study

22. Case Study

23. Case Study

24. Case Study

25. Case Study

26. Case Study

27. Compactness rate

28. Compactness rate shape index

29. Compactness rate

30. Case Study

31. Changes in area/perimeter ratio

32. Case Study

33. Case Study R3, R4 >35%

34. Case Study <150m

35. Case Study < < Real contiguity Ideal contiguity Without contiguity Pignola

36. Case Study Real contiguity<Ideal contiguity<Without contiguity Avigliano Lauria

37. Case Study Without contiguity<Real contiguity<Ideal contiguity Potenza

38. Case Study Potenza

39. Case Study Potenza

40. Case Study

41. Case Study Rough classification

42. Case Study

43. Case Study

44. Case Study

45. Case Study Lauria Without contiguity

46. Case Study Real contiguity <Ideal contiguity Lauria

47. Case Study Picerno Without contiguity

48. Case Study Real contiguity <Ideal contiguity Picerno