Antonio Sala, Alicia Esparza, Carlos Ariño, Jose V. Roig


This paper discusses how to encode fuzzy knowledge bases for diagnostic tasks (i.e., list of symptoms produced by each fault, in linguistic terms described by fuzzy sets) as constrained optimisation problems. The proposed setting allows more flexibility than some fuzzy-logic inference rulebases in the specification of the diagnostic rules in a transparent, user-understandable way (in a first approximation, rules map to zeros and ones in a matrix), using widely-known techniques such as linear and quadratic programming.


  1. Angeli, C. (1999). Online expert system for fault diagnosis in hydraulic systems. Expert Systems, 16:115-120.
  2. Ayoubi, M. and Isermann, R. (1997). Neuro-fuzzy systems for diagnosis. Fuzzy Sets and Systems, 89(3):289-307.
  3. Berger, J. (1985). Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, London.
  4. Blanke, M., Kinnaert, M., Lunze, J., and Staroswiecki, M., editors (2003). Diagnosis and Fault-Tolerant Control. Springer, London.
  5. Carrasco, E. and et. al., J. R. (2004). Diagnosis of acidification states in an anaerobic wastewater treatment plant using a fuzzy-based expert system. Control Engineering Practice, 12(1):59-64.
  6. Castillo, E., Gutierrez, J., and Hadi, A. (1997). Expert Systems and Probabilistic Network Models. Springer, London.
  7. Chiang, L., Russell, E., and Braatz, R. (2001). Fault Detection and Diagnosis in Industrial Systems. SpringerVerlag.
  8. Chow, M., Sharpe, R., and Hung, J. (1993). On the application and design consideration of artificial neural network fault detectors. IEEE Trans. Industrial Electronics, 40:181-198.
  9. Dubois, D. and Prade, H. (2004). Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems, 144(1):3-23.
  10. Gass, S. (2003). Linear Programming: methods and applications. Dover, 5th edition.
  11. Jarvensivu, M., Juuso, E., and Ahavac, O. (2001). Intelligent control of a rotary kiln fired with producer gas generated from biomass. Eng. Applic. Artif. Intelligence, 14:629-653.
  12. Jie, Z. and Morris, J. (1996). Process modelling and fault diagnosis using fuzzy neural networks. Fuzzy Sets and Systems, 79(1):127-140.
  13. Juuso, E. (1999). Fuzzy control in process industry: the linguistic equation approach. In Verbruggen, H., Zimmermann, H.-J., and Babuska, R., editors, Fuzzy Algorithms for Control, pages 243-300. Kluwer, Boston.
  14. Khalil, H. (2002). Nonlinear Systems. Prentice Hall, third edition.
  15. Kruse, R., Schwecke, E., and Heinsohn, J., editors (1991). Uncertainty and vagueness in Knowledge Based Systems: Numerical Methods (Artificial Intelligence). Springer-Verlag.
  16. Kyburg, H. (1988). Higher order probabilities and intervals. Int. J. Approximate Reasoning, 2:195-209.
  17. Meyer, C. (2001). Matrix Analysis and Applied Linear Algebra. Society for Industrial & Applied Mathematics (SIAM).
  18. Russell, S. and Norvig, P. (2003). Artificial Intelligence: a modern approach. Prentice-Hall, 2nd edition.
  19. Sala, A. and Albertos, P. (2001). Inference error minimisation: Fuzzy modelling of ambiguous functions. Fuzzy Sets and Systems, 121(1):95-111.
  20. Shafer, G. and Pearl, J., editors (1990). Readings in uncertain reasoning. Morgan Kauffman, San Mateo (CA), USA.
  21. Sierksma, G. (2001). Linear and Integer Programming: Theory and Practice. Marcel Dekker Pub., New York, 2nd edition.
  22. Timmer, J. (2000). Parameter estimation in nonlinear stochastic differential equations. Chaos, Solitons and Fractals, 11(15):2571-2578.
  23. Yamada, K. (2004). Diagnosis under compound effects and multiple causes by means of the conditional causal possibility approach. Fuzzy Sets and Systems, 145:183-212.
  24. Yao, J. and Yao, J. (2001). Fuzzy decision making for medical diagnosis based on fuzzy number and compositional rule of inference. Fuzzy Sets and Systems, 120:351-366.

Paper Citation

in Harvard Style

Sala A., Esparza A., Ariño C. and V. Roig J. (2006). ENCODING FUZZY DIAGNOSIS RULES AS OPTIMISATION PROBLEMS . In Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-972-8865-59-7, pages 34-39. DOI: 10.5220/0001203100340039

in Bibtex Style

author={Antonio Sala and Alicia Esparza and Carlos Ariño and Jose V. Roig},
booktitle={Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},

in EndNote Style

JO - Proceedings of the Third International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
SN - 978-972-8865-59-7
AU - Sala A.
AU - Esparza A.
AU - Ariño C.
AU - V. Roig J.
PY - 2006
SP - 34
EP - 39
DO - 10.5220/0001203100340039