REASONING UNDER UNCERTAINTY WITH BAYESIAN BELIEF NETWORKS ENHANCED WITH ROUGH SETS

Authors

  • Andrew J. Kornecki
  • Slawomir T. Wierzchon
  • Janusz Zalewski

DOI:

https://doi.org/10.47839/ijc.12.1.584

Keywords:

Bayesian Belief Networks, Rough Sets, Decision Uncertainty, Soft Computing.

Abstract

The objective of this paper is to present a new approach to reasoning under uncertainty, based on the use of Bayesian belief networks (BBN’s) enhanced with rough sets. The role of rough sets is to provide additional reasoning to assist a BBN in the inference process, in cases of missing data or difficulties with assessing the values of related probabilities. The basic concepts of both theories, BBN’s and rough sets, are briefly introduced, with examples showing how they have been traditionally used to reason under uncertainty. Two case studies from the authors’ own research are discussed: one based on the evaluation of software tool quality for use in real-time safety-critical applications, and another based on assisting the decision maker in taking the right course of action, in real time, in the naval military exercise. The use of corresponding public domain software packages based on BBN’s and rough sets is outlined, and their application for real-time reasoning in processes under uncertainty is presented.

References

N.E. Fenton, M. Neil, The use of Bayes and causal modelling in decision making, uncertainty and risk, Agena Risk White Paper, June 2011. Available at: http://www.agenarisk.com/resources/white_papers/fenton_neil_white_paper2011.pdf.

F.V. Jensen, T.D. Nielsen, Bayesian Networks and Decision Graphs. Second Edition, Springer-Verlag, 2007.

W.J. Dawsey, Bayesian belief networks to integrate monitoring evidence of water distribution system contamination, Master Thesis, University of Illinois at Urbana-Champaign, February 2012.

M. Azhdari, N. Mehranbod, Application of Bayesian belief networks to fault detection and diagnosis of industrial processes, Proc. ICCCE 2010, Intern. Conf. on Chemistry and Chemical Engineering, Kyoto, Japan, August 1-3, 2010, pp. 92-96.

P. Newham et al., Fog forecasting at Melbourne airport using Bayesian networks, Proc. Fourth Intern. Conf. on Fog, Fog Collection and Dew, Santiago, Chile, July 22-27, 2007, pp. 291-294.

N. Fenton et al., Predicting software defects in varying development lifecycles using Bayesian nets, Information and Software Technology, (49) 1 (2007), pp. 32-43.

C. Lee et al., Inferring certification metrics of package software using Bayesian belief networks, Proc. ICIC 2006 – Intern. Conf. on Intelligent Computing, Kunming, China, August 16-19, 2006, pp. 915-920.

A. Leger et al., Predicting hospital admission for Emergency Department patients using a Bayesian network, Proc. AMIA Annual Symposium. Washington, DC, October 22-26, 2005, p. 1022.

S. Ferrari, A. Vaghi, Multisensor fusion for landmine detection by a Bayesian network approach, Proc. ECSC – 3rd European Conf. on Structural Control, Vienna, Austria, July 12-15, 2004.

A.K.T. Hui et al., A Bayesian belief network model and tool to evaluate risk and impact in software development projects, Proc. RAMS 2004 – Annual IEEE Reliability and Maintainability Symposium, Los Angeles, Calif., January 26-29, 2004, pp. 297-301.

M. Neil, B. Mancom, R. Shaw, Modelling an air traffic control environment using Bayesian belief networks, Proc. ISSC’03 – 21st Intern. System Safety Conf., Ottawa, Ontario, August 4-8, 2003.

K. Sachs et al., Bayesian network approach to cell signaling pathway modeling, Science STKE, 148, PE38, 2002.

A. Helminen, Reliability Estimation of Safety-Critical Software-Based Systems Using Bayesian Networks, Report STUK-YTO-TR 178, Radiation and Nuclear Safety Authority, Helsinki, Finland, 2001.

G. Dahll, B.A. Gran, The use of Bayesian belief nets in safety assessment of software based systems, International Journal of General Systems, (29) 2 (2000), pp. 205-229.

N.E. Fenton, M. Neil, Bayesian belief nets: a causal model for predicting defect rates and resource requirements, Software Testing and Quality Engineering, (2) 1 (2000), pp. 48-53.

P. Smets, Belief functions: the disjunctive rule of combination and the generalized Bayesian theorem, International Journal on Approximate Reasoning, (9) 1 (1993), pp. 1-35.

J.A. Bernardo, A.F.M. Smith, Bayesian Theory, John Wiley and Sons, 1994.

Z. Pawlak, Rough Sets, International Journal of Information and Computer Sciences, (11) 5 (1982), pp. 341-356, Available at: http://chc60.fgcu.edu/Images/articles/PawlakOriginal.pdf

Z. Pawlak, Rough Sets – Theoretical Aspects of Reasoning about Data, Kluwer Academic Publishers, 1991.

Ji Zhang et al., Neighborhood rough sets for dynamic data mining, Intern. Journal of Intelligent Systems, (27) 4 (2012), pp. 317-342.

Y. Li et al., A generalized model of covering rough sets and its application in medical diagnosis, Proc. ICMLS 2010, Intern. Conf. on Machine Learning and Cybernetics, Qingdao, China, July 11-14, 2010, pp. 145-150.

M. Bit, T. Beaubouef, Rough set uncertainty for robotic systems, Journal of Computing Sciences in Colleges, (23) 6 (2008), pp. 126-132.

G. Ilczuk, A. Wakulicz-Deja, Visualization of rough set decision rules for medical diagnosis systems, Proc. RSFDGrC 2007 – 11th Intern. Conf. on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, Toronto, Canada, May 14-16, 2007, pp. 371-378.

J. Stefanowski, An empirical study of using rule induction and rough sets to software cost estimation, Fundamenta Informaticae, (71) 1 (2006), pp. 63-82.

P.A. Laplante, C.J. Neill, Modeling uncertainty in software engineering using rough sets, Innovations in Systems and Software Engineering – A NASA Journal, (1) 1 (2005), pp. 71-78.

Z. Li, G. Ruhe, Uncertainty handling in tabular-based requirements using rough sets, Proc. RSFDGrC 2005 – Intern. Conf. on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, Regina, Canada, 31 August – 3 September, 2005.

R. Wasniowski, A framework for software safety analysis with rough sets, Proceedings of the 4th WSEAS Intern. Conf. on Software Engineering, Parallel & Distributed Systems, Salzburg, Austria, February 13-15, 2004.

J.F. Peters, H. Feng, S. Ramanna, Adaptive granular control of an HVDC system: A rough set approach, Proc. of RSFDGrC 2003 – 7th Intern. Conf. on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, Chingqing, China, May 26-29, 2000, pp. 213-220.

N. Meskens, P. Levecq, F. Lebon, Multivariate analysis and rough sets: two approaches for software-quality analysis, International Transactions in Operational Research, (9) 3 (2002), pp. 353-369.

L. Shen et al., Fault diagnosis using rough sets theory, Computers in Industry, (43) 1 (2000), pp. 61-72.

J. Zalewski, Z. Wojcik, Use of Artificial Intelligence Techniques for Prognostics: New Application of Rough Sets, Intern. Journal of Computing, (11) 1 (2012), pp. 73-81.

T. Bayes, Essay towards solving a problem in the doctrine of chances, Philosophical Transactions of the Royal Society of London, 53, (1763), pp. 370-418.

J. Pearl, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference, Morgan-Kaufmann, 1988.

Norsys Software Corporation. Netica. Version 4.08, Vancouver, Canada, URL: http://www.norsys.com

Hugin Expert A/S. Hugin Developer Software Package. Aalborg, Denmark. URL: http://www.hugin.com/

M. Kryszkiewicz, Comparative study of alternative types of knowledge reduction. International J. of Intelligent Systems, (16) 1 (2001), pp. 105-120.

W. Ziarko, Rough sets as a methodology for data mining, In: Rough Sets in Knowledge Discovery 1: Methodology and Applications. Physica-Verlag, 1998, pp. 554-576.

J. Komorowski, L. Polkowski, A. Skowron, Rough sets: a tutorial. In: S.K. Pal and A.Skowron (Eds.), Rough-Fuzzy Hybridization: A New Method for Decision Making, Springer-Verlag, 1998.

A. Ohrn, J. Komorowski, J. Rosetta, A rough set toolkit for analysis of data, Proc. RSSC’97 – Third Intern. Joint Conf. on Information Sciences, Fifth Inter. Workshop on Rough Sets and Soft Computing, Durham, NC, (3) (1997), pp. 403-407.

J. Grzymala-Busse. LERS – A system for learning from examples based on rough sets. In: R. Slowinski (Ed.), Intelligent Decision Support: Handbook of Applications and Advances of Rough Set Theory (pp. 3-18), Kluwer Academic Publishers, 1992.

J. Grzymala-Busse, Three approaches to missing attribute values – a rough set perspective, Proc. Workshop on Foundation of Data Mining – 4th IEEE Intern. Conf. on Data Mining, Brighton, UK, November 1-4, 2004.

I.E. Chen-Jimenez, A. Kornecki, J. Zalewski, Software safety analysis using rough sets, Proc. IEEE Southeastcon’98, Orlando, Fla., April 24–26, 1998, pp. 15-19.

A. Kornecki, J. Zalewski, Experimental evaluation of software development tools for safety-critical real-time systems, Innovations in Systems and Software Engineering – A NASA Journal, (1) 2 (2005), pp. 176-188.

A. Kornecki, J. Zalewski, Software development tools qualification from the DO-178B certification perspective, Crosstalk – The Journal of Defense Software Engineering, (19) 4 (2006), pp. 19-22.

M. Neil, N. Fenton, Predicting software quality using Bayesian belief networks, Proc. SEW-21 – Annual NASA Goddard Software Engineering Workshop, Washington, DC, December 4-5, 1996, pp. 217-230.

B.A. Gran et al., Estimating dependability of programmable systems using BBNs, Proc. SAFECOMP 2000 – 19th Intern. Conference on Computer Safety, Reliability and Security, Rotterdam, The Netherlands, October 24-27, 2000, pp. 309-320.

K.A. Delic, F. Mazzanti, L. Strigini, Formalising engineering judgement on software dependability via belief networks, Proc. DCCA-6 – 6th IFIP Intern. Working Conf. on Dependable Computing for Critical Applications, Garmisch-Partenkirchen, Germany, March 5-7, 1997, pp. 291-305.

A. Kornecki, N. Brixius, J. Zalewski, Assessment of Software Development Tools for Safety-Critical, Real-Time Systems, Report DOT/FAA/AR-06/36, Federal Aviation Administration, Washington, DC, 2007.

B. Das, Representing Uncertainties Using Bayesian Networks, Report DSTO-TR-0918, Defence Science and Technology Organisation, Electronics and Surveillance Research Laboratory, Sydney, Australia, 1999.

R.G. Brown, P.Y.C. Hwang, Introduction to Random Signals and Applied Kalman Filtering, Third Edition, John Wiley and Sons, 1997.

Downloads

Published

2014-08-01

How to Cite

Kornecki, A. J., Wierzchon, S. T., & Zalewski, J. (2014). REASONING UNDER UNCERTAINTY WITH BAYESIAN BELIEF NETWORKS ENHANCED WITH ROUGH SETS. International Journal of Computing, 12(1), 16-31. https://doi.org/10.47839/ijc.12.1.584

Issue

Section

Articles