Abstract
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.
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References
Chiang, L., Russell, E., Braatz, R.: Fault Detection and Diagnosis in Industrial Systems. Springer-Verlag, London, UK (2001)
Blanke, M., Kinnaert, M., Lunze, J., Staroswiecki, M., eds.: Diagnosis and Fault-Tolerant Control. Springer, London (2003)
Timmer, J.: Parameter estimation in nonlinear stochastic differential equations. Chaos, Solitons and Fractals 11 (2000) 2571–2578
Khalil, H.: Nonlinear Systems. 3rd edn. Prentice Hall, New Jersey, USA (2002)
Berger, J.: Statistical Decision Theory and Bayesian Analysis. Springer-Verlag, London (1985)
Angeli, C.: Online expert system for fault diagnosis in hydraulic systems. Expert Systems 16 (1999) 115–120
Carrasco, E. et. al.: Diagnosis of acidification states in an anaerobic wastewater treatment plant using a fuzzy-based expert system. Control Engineering Practice 12 (2004) 59–64
Kruse, R., Schwecke, E., Heinsohn, J., eds.: Uncertainty and vagueness in knowledge based systems: numerical methods (artificial intelligence). Springer-Verlag, Berlin, DE (1991)
Shafer, G., Pearl, J., eds.: Readings in uncertain reasoning. Morgan Kauffman, San Mateo (CA), USA (1990)
Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems 144 (2004) 3–23
Yamada, K.: Diagnosis under compound effects and multiple causes by means of the conditional causal possibility approach. Fuzzy Sets and Systems 145 (2004) 183–212
Castillo, E., Gutierrez, J., Hadi, A.: Expert Systems and Probabilistic Network Models. Springer, London (1997)
Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach. 2nd edn. Prentice-Hall, New Jersey, USA (2003)
Kyburg, H.: Higher order probabilities and intervals. International Journal of Approximate Reasoning 2 (1988) 195–209
Ayoubi, M., Isermann, R.: Neuro-fuzzy systems for diagnosis. Fuzzy Sets and Systems 89 (1997) 289–307
Jie, Z., Morris, J.: Process modelling and fault diagnosis using fuzzy neural networks. Fuzzy Sets and Systems 79 (1996) 127–140
Juuso, E.: Fuzzy control in process industry: the linguistic equation approach. In Verbruggen, H., Zimmermann, H.J., Babuska, R., eds.: Fuzzy Algorithms for Control. Kluwer, Boston (1999) 243–300
Sala, A., Albertos, P.: Inference error minimisation: Fuzzy modelling of ambiguous functions. Fuzzy Sets and Systems 121 (2001) 95–111
Sierksma, G.: Linear and Integer Programming: Theory and Practice. 2nd edn. Marcel Dekker Pub., New York (2001)
Gass, S.: Linear Programming: methods and applications. 5th edn. Dover, Mineola, NY, USA (2003)
Chow, M., Sharpe, R., Hung, J.: On the application and design consideration of artificial neural network fault detectors. {IEEE} Transactions on Industrial Electronics 40 (1993) 181–198
Yao, J., Yao, J.: Fuzzy decision making for medical diagnosis based on fuzzy number and compositional rule of inference. Fuzzy Sets and Systems 120 (2001) 351–366
Meyer, C.: Matrix Analysis and Applied Linear Algebra. Society for Industrial & Applied Mathematics {(SIAM)} (2001)
Jarvensivu, M., Juuso, E., Ahavac, O.: Intelligent control of a rotary kiln fired with producer gas generated from biomass. Engineering Applications of Artificial Intelligence 14 (2001) 629–653
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Sala, A., Esparza, A., Ariño, C., Roig, J.V. (2008). Encoding Fuzzy Diagnosis Rules as Optimisation Problems. In: Cetto, J.A., Ferrier, JL., Costa dias Pereira, J., Filipe, J. (eds) Informatics in Control Automation and Robotics. Lecture Notes Electrical Engineering, vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79142-3_5
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DOI: https://doi.org/10.1007/978-3-540-79142-3_5
Publisher Name: Springer, Berlin, Heidelberg
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