Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy) - Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Cinzia Zotta, Lucia Tilio, Maria Danese, Beniamino Murgante

1. Fabrizio Gizzi, Nicola Masini Maria Rosaria Potenza, Cinzia Zotta, Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy) Laboratory of Urban and Territorial Systems, University of Basilicata, Italy Lucia Tilio, Maria Danese, Beniamino Murgante Archaeological and monumental heritage institute, National Research Council, Italy

2. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Introduction Analysis concerning earthquake events are normally strictly related to damage survey. It is evident that documentary sources concerning urban historical damage can provide useful information for seismic microzonation. This research concerns historical earthquake (1930) damage related to towns of a seismic area of southern Italy (Vulture district, Basilicata). 4,000 dossiers compiled by the Special Office of Civil Engineers have been analyzed.

4. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set Let U be a nonempty finite set of objects called the universe Let A be a nonempty finite set of attributes

5. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set U a 1 a 2 a 3 x 1 2 1 3 X 2 3 2 1 X 3 2 1 3 X 4 2 2 3 X 5 1 1 4 X 6 1 1 2 X 7 3 2 1 X 8 1 1 4 X 9 2 1 3 x 10 3 2 1

6. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set A decision system is an information system in which the values of a special decision attribute classify the cases U a 1 a 2 a 3 d 1 x 1 2 1 3 1 X 2 3 2 1 4 X 3 2 1 3 5 X 4 2 2 3 2 X 5 1 1 4 2 X 6 1 1 2 4 X 7 3 2 1 1 X 8 1 1 4 2 X 9 2 1 3 3 x 10 3 2 1 2

8. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set Equivalence classes Lower Approximation Upper Approximation Boundary Region If BX =  then the set X is Crisp If BX ≠  then the set X is Rough Accuracy

9. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set In order to have an idea about how much an object x belongs to X we define rough membership. The rough membership function quantifies the degree of relative overlap between the set X and the equivalence class to which x belongs.

10. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set A reduct eliminate redundant attributes A reduct is a minimal set of attributes (from the whole attributes set) that preserves the partitioning of the of U and therefore the original classes.

11. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set Color Size Shape Accept x 1 G Small Square Yes x 2 B Medium Triangular No x 3 R Small Rectangular No x 4 G Medium Rectangular Yes x 5 G Small Square Yes x 6 Y Large Round No x 7 Y Medium Triangular Yes x 8 B Medium Triangular No

12. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set U = { x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 , x 8 } A = {color, size, shape} color(green, blue, red, yellow) size(small, large, medium) shape(square, round, triangular, rectangular) U/color = {( x 1 , x 4 , x 5 ), ( x 2 , x 8 ), ( x 3 ), ( x 6 , x 7 )} U/size = {( x 1 , x 3 , x 5 ), ( x 6 ), ( x 2 , x 4 , x 7 , x 8 )} U/shape = {( x 1 , x 5 ), ( x 6 ), ( x 2 , x 7 , x 8 ), ( x 3 , x 4 )}

13. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set U/ IND (A) = {( x 1 , x 5 ), ( x 2 , x 8 ), ( x 3 ), ( x 4 ), ( x 6 ) , ( x 7 )} U/ IND (A –{color}) = {( x 1 , x 5 ), ( x 2 , x 7 , x 8 ), ( x 3 ), ( x 4 ) ( x 6 )}  U/ IND (A) U/ IND (A –{size}) = {( x 1 , x 5 ), ( x 2 , x 8 ), ( x 3 ), ( x 4 ), ( x 6 ) , ( x 7 )} = U/ IND (A) U/ IND (A –{shape}) = {( x 1 , x 5 ), ( x 2 , x 8 ), ( x 3 ), ( x 4 ), ( x 6 ) , ( x 7 )} = U/ IND (A) RED(A) = {(color, size), (color, shape)} CORE(A) = {color}

14. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Rough Set Rough Set Analysis allows to identify patterns and to extract relations, identifying cause-effect relations. Identified patterns are represented through a decisional rule set, where rules are expressed in the “if…then” form. Objects are assigned to a decision class if it satisfies the conditions of an identified rule; rule strength is determined by number of objects satisfying that condition; at the same time, this number of points also gives a measure of uncertainty into decision class assignment. IF attribute1 ….. AND IF attribute2…. AND IF… THEN decision attribute is … Rules can be exact, when they are characterized by an univocal consequence, and supported only by objects from the lower approximation of the corresponding decision class, or approximate, when they are characterized by not univocal consequence, and supported only by objects from the boundaries of the corresponding decision class

15. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case Earthquake 1930 Buildings damage survey  738 Attributes  37 Which relationship between damage and reconstruction ? Rapolla

16. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case EUROPEAN MACROSEISMIC SCALE

17. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case Form used in order to record and to analyse the documentary data SURVEYS BASED ON FORM

18. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case a lot of information about reconstruction…

19. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case Building ID Reference (map, envelope, ...) Building demolition Type of Building (religious,public...) Withdrawn subvention Costs of works Effectively Funded Costs of works accounted Estimated costs of works Start and End Work Date Real estate values of Building Owner Annual Income Data concerning information about the damage, the post-seismic repairing procedures with buildings techniques description of the housing units and technical-economic-administrative data . What kind of information? Walls demolition Floors demolition Vault demolition New wall New Floors Toothing projects Shearing stress of masonry Cuci-Scuci Damage description Declared Destroyed Damage class EMS Adoption of tie-beam Roof rebuilding Cracks rebuilding Test date

20. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case – the analysis RESULTS Six analysis, testing different datasets, in order to increase quality of classification Decision Attribute Quality of classification # of Atoms # of Reducts # of attributes in Core Analysis 0 DANNO EMS 0,2665 189 1 17 Analysis 1 0,3887 287 8 9 Analysis 2 0,3874 281 12 4 Analysis 3 0,7084 264 12 8 Analysis 4 0,7411 276 1 9 Analysis 5 0,7057 265 2 8 Rapolla Number of Really analyzed buildings 728 316 attributes 29 16

21. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case – the analysis Quotient of cardinalities of all lower approximation of the classes in which the object set is classified and the cardinality of the object set It is determined by application of indiscernibility relation. Atoms are the elementary sets. Decision Attribute Quality of classification # of Atoms # of Reducts # of attributes in Core Analysis 5 DANNO EMS 0,7057 265 2 8

22. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case IF attribute1 ….. AND IF attribute2…. AND IF… THEN decision attribute is … } CONDITIONAL PART ASSIGNMENT }

23. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules reading RULES MAPPED ON GIS AND GROUPED ACCORDING TO DAMAGE CLASSIFICATION

24. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules reading RULES MAPPED ON GIS AND GROUPED ACCORDING TO DAMAGE CLASSIFICATION

25. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules reading RULES MAPPED ON GIS AND GROUPED ACCORDING TO DAMAGE CLASSIFICATION

26. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules reading RULES MAPPED ON GIS AND GROUPED ACCORDING TO DAMAGE CLASSIFICATION

27. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules interpretation There is a certain number of rules (25/88) that present a clear discrepancy into damage level attribution. The analysis permits the identification of such discrepancy and a possible interpretation: differences in damage distribution are not spatially clusterized, but they concerns areas having different social and building features (rich and poor owners, big and small housing, building well preserved and lacking of maintenance ect.)

28. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules interpretation Clear discrepancy into damage level attribution: Here, the cases of doubt between d2 and d3 EXAMPLE: Rule 13 IF “impcont<3” AND “imprev<3” AND “valimm<4”… THEN “danno_ems=d2”

29. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules interpretation Clear discrepancy into damage level attribution: Here, the cases of doubt between d3 and d2 EXAMPLE: Rule 40 IF “valimm<1” AND “intcopertu in [0, dem/ric]” AND “scucicuci=si” AND “demsolai=0” AND “durlav<28”THEN “danno_ems=d2”

30. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules interpretation Clear discrepancy into damage level attribution: Here, the cases of doubt between d4 and d2 EXAMPLE: Rule 79 IF “nuovisolai=travi_acc/tav” AND “scucicuci=0” AND “durlav>=102”THEN “danno_ems=d4”

31. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules interpretation Clear discrepancy into damage level attribution: Here, the cases of doubt between d4 and d3 EXAMPLE: Rule 67 IF “impper>=5” AND “impcont=[2,4]” AND “durlav<34” THEN “danno_ems=d4”

32. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Study Case: rules interpretation Changes in damage classification seem not to be due to voluntary human influences (e.g. acquaintance with technicians to get increase of damage attribution by favoritism) rather differences may be imputable to other factors, among which: Why discrepancy in damage level attribution?

34. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan A step towards future development… New study area TOWN Number of buildings Buildings really analyzed Melfi 2256 1190 Rapolla 728 316 Rionero 3373 1213 Ripacandida 754 374 San Fele 1200 175

35. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan A step towards future development… Preliminary results: # of buildings # of analysed buildings Quality of classification Number of Atoms Number of Reducts # Attributes in Core # of Rules # of Exact Rules # of Approximate Rules Melfi 2256 1190 0.4538 557 1 4 270 207 63 Rapolla 728 316 0.7057 235 1 7 111 99 12 Rionero 3373 1213 0.4361 585 1 4 340 252 88 Ripacandida 754 374 0.7406 279 1 7 99 89 10 San Fele 1200 175 0.7371 75 1 5 37 31 6

36. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan A step towards future development… Preliminary results: Interpretation of rules producing an overestimation and an underestimation of damage level in Ripacandida

37. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan A step towards future development… Preliminary results: Interpretation of rules producing an overestimation and an underestimation of damage level in Rionero

38. Assessing macroseismic data reliability through Rough Set Theory: the case of Rapolla (Basilicata, southern Italy), F. Gizzi, N. Masini, M.R. Potenza, C. Zotta, L. Tilio, M. Danese, B. Murgante International Conference on Computational Science and Its Applications March 23 – 26, Fukoka, Japan Future development Further extension of study area It is known that during an earthquake the damage to buildings with comparable features can differ enormously between points. In a wider area it could be interesting to analyze also effects of geological surface.