Example Applications of Rough
Sets Theory – A Survey
Christopher Chretien
Laurentian University
Sudbury, Ontario
Canada
October 2002
Introduction
Research on the application of Rough
Sets Theory
 Discovering possible areas of application
 Further 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 multicylinder 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
characteristics
Normal state
 Intake valve clearance is too small
 Intake valve clearance is too large
 Exhaust valve clearance is too large

Fault Diagnosis using Rough Sets
Theory

3 sampling points selected to collect
vibration signals
1st cylinder head
 2nd cylinder head
 centre 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 attributes
Frequency domain attributes: IF, CG
 Time domain attributes: IT, σ, Dx, α4

18 attributes for decision table
 1 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 model

Project Planning
 Specification of requirements
 Design
 Implementation and integration
 Verification and validation
 Operation and maintenance

Software Safety Analysis using
Rough Sets
Software Safety Analysis using
Rough Sets
Software Safety Analysis using
Rough Sets

8 student teams developing safetyrelated software
Device control over the internet
 Elevator controller
 Air traffic control system
 System 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 prediction

ETEVA
Database Marketing
 Financial 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 Model
An 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

Corpus
Monomorphemic words
 At least 2 non-schwa syllables
 Nouns
 242 words

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

Using Rough Set Theory to Predict
German Word Stress

1st experiment


2nd experiment


Stress assignment operates from right to left
Estimate predictive accuracy
3rd experiment

Remove 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 GAs
Job shop scheduling
 Training 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 scheme
1.
2.
3.
Both uh and uk are in the same lower
approximation A(Xi).
Object uh is in a lower approximation and
uk is in the corresponding upper
approximation UA(Xi)
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 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

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

Conclusion
Triggering a better understanding of
Rough Sets Theory
 Opening eyes to different fields of
application
