1. Example Applications of Rough Sets Theory – A Survey Christopher Chretien Laurentian University Sudbury, Ontario Canada October 2002

2. Introduction Research on the application of Rough Sets Theory Discovering possible areas of application Further understanding of Rough Sets Theory usage

3. References Lixiang Shen, Francis E. H. Tay, Liangsheng Qu and Yudi Shen (2000), Fault Diagnosis using Rough Sets Theory, Computers in Industry, vol. 43, Issue 1, 1 August 2000, pp.61-72., URL:www.geocities.com/roughset/Fault_diagnosis_using_rough_sets_theory.pdfwww.geocities.com/roughset/Fault_diagnosis_using_rough_sets_theory.pdf Israel E. Chen-Jimenez, Andrew Kornecki, Janusz Zalewski, Software Safety Analysis Using Rough Sets, URL:http://www-ece.engr.ucf.edu/~jza/classes/6885/rough.pshttp://www-ece.engr.ucf.edu/~jza/classes/6885/rough.ps Francis E. H. Tay and Lixiang Shen (2002), Economic and Financial Prediction using Rough Sets Model, European Journal of Operational Research 141, pp.643-661, URL:http://www.geocities.com/roughset/EJOR.pdfhttp://www.geocities.com/roughset/EJOR.pdf Pawan Lingras (2001), Unsupervised Rough Set Classification Using GAs Journal of Intelligent Information Systems, 16, 215–228, found on: CiteSeer, URL:http://citeseer.nj.nec.com/cshttp://citeseer.nj.nec.com/cs Rapp, S., Jessen, M. and Dogil, G. (1994). Using Rough Sets Theory to Predict German Word Stress. in: Nebel, B. and Dreschler-Fischer, L. (Eds.) KI-94: Advances in Artificial Intelligence, Lecture Notes in Artificial Intelligence 861, Springer-Verlag, URL:www.ims.uni-stuttgart.de/~rapp/ki94full.pswww.ims.uni-stuttgart.de/~rapp/ki94full.ps

4. Fault Diagnosis using Rough Sets Theory Diagnosis of a valve fault for a multi- cylinder diesel engine Rough Sets Theory is used to analyze the decision table composed of attributes extracted from the vibration signals

5. Fault Diagnosis using Rough Sets Theory 4 states are studied among the signal characteristics Normal state Intake valve clearance is too small Intake valve clearance is too large Exhaust valve clearance is too large

6. Fault Diagnosis using Rough Sets Theory 3 sampling points selected to collect vibration signals 1 st cylinder head 2 nd cylinder head centre of the piston stroke on the surface of the cylinder block

7. Fault Diagnosis using Rough Sets Theory

10. 6 attributes Frequency domain attributes: IF, CG Time domain attributes: IT, σ, D x, α 4 18 attributes for decision table 1 decision attribute with 4 possible values based on states

11. Software Safety Analysis using Rough Sets Investigates the safety aspects of computer software in safety-critical applications Assessment of software safety using qualitative evaluations

12. Software Safety Analysis using Rough Sets Use of checklists to collect data on software quality Waterfall model Project Planning Specification of requirements Design Implementation and integration Verification and validation Operation and maintenance

13. Software Safety Analysis using Rough Sets

15. 8 student teams developing safety- related software Device control over the internet Elevator controller Air traffic control system System satellite control system

16. Software Safety Analysis using Rough Sets 150 questions about the first 5 phases of the waterfall model Overall safety level for 6 of the 8 projects was around 60%

17. Economic and Financial Prediction using Rough Sets Model Applications of Rough Sets model in economic and financial prediction Emphasis on main areas of business failure prediction, database marketing and financial investment

18. Economic and Financial Prediction using Rough Sets Model Business failure prediction ETEVA Database Marketing Financial Investment TSE

19. Economic and Financial Prediction using Rough Sets Model

21. Using Rough Set Theory to Predict German Word Stress Prediction of German word stress by extracting symbolic rules from sample data Symbolic rules are induced with a machine learning approach based on Rough Sets Theory

22. Using Rough Set Theory to Predict German Word Stress Variable Precision Rough Sets Model An elementary class belongs to R β X iff a (100% - β) majority of it’s elements belongs to X An elementary class does not belong to UR β X iff a (100% - β) majority of its elements does not belong to X

23. Using Rough Set Theory to Predict German Word Stress Corpus Monomorphemic words At least 2 non-schwa syllables Nouns 242 words

24. Using Rough Set Theory to Predict German Word Stress Attributes: Typ, Onset, Hoeche, Laenge, Spannung, Coda 36 attributes in total Attributes aligned ‘from right to left’ Decision attribute with possible values of final, penult and antepenult

25. Using Rough Set Theory to Predict German Word Stress 1 st experiment Stress assignment operates from right to left 2 nd experiment Estimate predictive accuracy 3 rd experiment Remove length information

26. Unsupervised Rough Set Classification using GAs Rough Set classification using Genetic Algorithms Highway classification based on predominant usage

27. Unsupervised Rough Set Classification using GAs Applications of GAs Job shop scheduling Training neural nets Image feature extraction Image feature identification

28. Unsupervised Rough Set Classification using GAs

32. Rough Set classification scheme 1. Both u h and u k are in the same lower approximation A(X i ). 2. Object u h is in a lower approximation and u k is in the corresponding upper approximation UA(X i ) 3. Both u h and u k are in the same upper approximation

33. Unsupervised Rough Set Classification using GAs Total error of rough set classification is the weighted sum of these errors

34. Unsupervised Rough Set Classification using GAs Rough classification of highways PTC sites Roads classified on the basis of trip purposes and trip length characteristics Classes: commuter, business, long distance and recreational highways Traffic patterns: hourly, daily, monthly

35. Unsupervised Rough Set Classification using GAs Experiment 264 monthly traffic patterns on Alberta highways (1987-1991) Rough genome consisted of 264 genes Classes: commuter/business, long distance, recreational

36. Conclusion Triggering a better understanding of Rough Sets Theory Opening eyes to different fields of application