Example Applications of Rough Sets Theory – A Survey

Christopher ChretienLaurentian UniversitySudbury, OntarioCanadaOctober 2002

Introduction

Research on the application of Rough Sets Theory

Discovering possible areas of applicationFurther understanding of Rough Sets

Theory usage

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.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.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.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/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.ps

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

Fault Diagnosis using Rough Sets Theory

4 states are studied among the signal characteristicsNormal state Intake valve clearance is too small Intake valve clearance is too largeExhaust valve clearance is too large

Fault Diagnosis using Rough Sets Theory

3 sampling points selected to collect vibration signals1st cylinder head2nd cylinder headcentre of the piston stroke on the surface of

the cylinder block

Fault Diagnosis using Rough Sets Theory

Fault Diagnosis using Rough Sets Theory

Fault Diagnosis using Rough Sets Theory

Fault Diagnosis using Rough Sets Theory

6 attributesFrequency domain attributes: IF, CGTime domain attributes: IT, σ, Dx, α4

18 attributes for decision table1 decision attribute with 4 possible

values based on states

Software Safety Analysis using Rough Sets

Investigates the safety aspects of computer software in safety-critical applications

Assessment of software safety using qualitative evaluations

Software Safety Analysis using Rough Sets

Use of checklists to collect data on software quality

Waterfall modelProject PlanningSpecification of requirementsDesign Implementation and integrationVerification and validationOperation and maintenance

Software Safety Analysis using Rough Sets

Software Safety Analysis using Rough Sets

Software Safety Analysis using Rough Sets

8 student teams developing safety-related softwareDevice control over the internetElevator controllerAir traffic control systemSystem satellite control system

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%

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

Economic and Financial Prediction using Rough Sets Model

Business failure predictionETEVA

Database MarketingFinancial Investment

TSE

Economic and Financial Prediction using Rough Sets Model

Economic and Financial Prediction using Rough Sets Model

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

Using Rough Set Theory to Predict German Word Stress

Variable Precision Rough Sets ModelAn elementary class belongs to RβX iff a

(100% - β) majority of it’s elements belongs to X

An elementary class does not belong to URβX iff a (100% - β) majority of its elements does not belong to X

Using Rough Set Theory to Predict German Word Stress

CorpusMonomorphemic wordsAt least 2 non-schwa syllablesNouns242 words

Using Rough Set Theory to Predict German Word Stress

Attributes: Typ, Onset, Hoeche, Laenge, Spannung, Coda

36 attributes in totalAttributes aligned ‘from right to left’Decision attribute with possible values of

final, penult and antepenult

Using Rough Set Theory to Predict German Word Stress

1st experimentStress assignment operates from right to left

2nd experimentEstimate predictive accuracy

3rd experimentRemove length information

Unsupervised Rough Set Classification using GAs

Rough Set classification using Genetic Algorithms

Highway classification based on predominant usage

Unsupervised Rough Set Classification using GAs

Applications of GAsJob shop schedulingTraining neural nets Image feature extraction Image feature identification

Unsupervised Rough Set Classification using GAs

Unsupervised Rough Set Classification using GAs

Unsupervised Rough Set Classification using GAs

Unsupervised Rough Set Classification using GAs

Unsupervised Rough Set Classification using GAs

Rough Set classification scheme1. Both uh and uk are in the same lower

approximation A(Xi).

2. Object uh is in a lower approximation and uk is in the corresponding upper approximation UA(Xi)

3. Both uh and uk are in the same upper approximation

Unsupervised Rough Set Classification using GAs

Total error of rough set classification is the weighted sum of these errors

Unsupervised Rough Set Classification using GAs

Rough classification of highwaysPTC sitesRoads classified on the basis of trip

purposes and trip length characteristicsClasses: commuter, business, long distance

and recreational highwaysTraffic patterns: hourly, daily, monthly

Unsupervised Rough Set Classification using GAs

Experiment264 monthly traffic patterns on Alberta

highways (1987-1991)Rough genome consisted of 264 genesClasses: commuter/business, long distance,

recreational

Conclusion

Triggering a better understanding of Rough Sets Theory

Opening eyes to different fields of application