Abstract
This chapter introduces fuzzy systems and how they can be cast into neuro-fuzzy system, which can be learned from data. It discusses how prior knowledge can be incorporated and how knowledge can be extracted from a data-driven neuro-fuzzy model. Different kinds of fuzzy systems are analyzed where the Takagi-Sugeno variant already builds bridges to the subsequent chapters on local linear modeling approaches. Different learning schemes for neuro-fuzzy models are discussed, and their principal ideas highlighted. The role of “defuzzification” or normalization in the context of learning and interpretability is discussed in detail.
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References
Alander, J.T.: An indexed bibliography of genetic algorithms and fuzzy systems. In: Pedrycz, W. (ed.) Fuzzy Evolutionary Computation, chapter 3.1, pp. 299–318. Kluwer Academic Publishers, Boston (1997). ftp: ftp.uwasa.fi, directory: /cs/report94-1, file: gaFUZZYbib.ps.Z
Babuška, R.: Fuzzy Modeling and Identification. Ph.D. thesis, Dept. of Control Engineering, Delft University of Technology, Delft, The Netherlands (1996)
Babuška, R., Verbruggen, H.B.: An overview of fuzzy modeling for control. Control Eng. Pract. 4(11), 1593–1606 (1996)
Bertram, T., Svaricek, F., Böhm, T., Kiendl, H., Pfeiffer, B.-M., Weber, M.: Fuzzy-Control. Zusammenstellung und Beschreibung wichtiger Begriffe. Automatisierungstechnik 42(7), 322–326 (1994)
Bossley, K.M.: Neurofuzzy Construction Algorithms. ISIS Technical Report ISIS-TR1, Department of Electronics and Computer Science, University of Southampton, Southampton, UK (1995)
Bossley, K.M.: Neurofuzzy Modelling Approaches in System Identification. Ph.D. thesis, Department of Electronics and Computer Science, University of Southampton, Southampton, UK (1997)
Bossley, K.M., Brown, M., Gunn, S.R., Harris, C.J.: Intelligent data modelling using neurofuzzy algorithms. In: IEE Colloquium on Industrial Applications of Intelligent Control, pp. 1–6, London, UK (1997)
Bothe, H.-H.: Fuzzy Logic: Einführung in Theorie und Anwendungen. Springer, Berlin (1993)
Branch, M.A., Grace, A.: MATLAB Optimization Toolbox User’s Guide, Version 1.5. The MATHWORKS Inc., Natick, MA (1998)
Brown, M., Harris, C.J.: Neurofuzzy Adaptive Modelling and Control. Prentice Hall, New York (1994)
Cordón, O., Herrera, F., Lozano, M.: A Classified Review on the Combination Fuzzy Logic: Genetic Algorithms Bibliography. Technical report, Department of Computer Science and Artificial Intelligence, Spain (1996)
Davis, L.: Handbook of Genetic Algorithms. van Nostrand Reinhold, New York (1991)
Driankov, D., Hellendoorn, H., Reinfrank, M.: An Introduction to Fuzzy Control. Springer, Berlin (1993)
Dubios, D., Prade, H.: Fuzzy Sets and Systems. Theory and Applications. Academic Press, New York (1980)
Halgamuge, S., Glesner, M.: Fuzzy neural fusion techniques for industrial applications. In: ACM Symposium on Applied Computing, Phoenix, USA (1994)
Hartman, E., Keeler, J.D.: Predicting the future: advantages of semilocal units. Neural Comput. 3(4), 566–578 (1991)
Herrera, F., Lozano, M., Verdegay, J.L.: A Learning for Fuzzy Control Rules Using Genetic Algorithms. Technical Report DECSAI-95108, Department of Computer Science and Artificial Intelligence, Spain (1995)
Hohensohn, J., Mendel, J.M.: Two-pass orthogonal least-squares algorithm to train and reduce fuzzy logic systems. In: IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pp. 696–700, Orlando, USA (1994)
Homaifar, A., McCormick, E.: Simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms. IEEE Trans. Fuzzy Syst. 3(2), 129–139 (1995)
Hunt, K.J., Haas, R., Murray-Smith, R.: Extending the functional equivalence of radial basis functions networks and fuzzy inference systems. IEEE Trans. Neural Netw. 7(3), 776–781 (1996)
Ishibuchi, H., Nozaki, K., Yamamoto, N., Tanaka, H.: Construction of fuzzy classification systems with rectangular fuzzy rules using genetic algorithms. Fuzzy Sets Syst. 65, 237–253 (1994)
Jager, R.: Fuzzy Logic in Control. Ph.D. thesis, Deft University of Technology, Delft, The Netherlands (1995)
Jang, J.-S.R., Sun, C.-T.: Functional equivalence between radial basis function networks and fuzzy inference systems. IEEE Trans. Neural Netw. 4(1), 156–159 (1993)
Kahlert, J., Frank, H.: Fuzzy-Logik und Fuzzy-Control. Vieweg, Braunschweig (1993)
Kavli, T.: ASMOD: an algorithm for adaptive spline modeling of observation data. Int. J. Control 58(4), 947–967 (1993)
Kecman, V., Pfeiffer, B.-M.: Exploiting the structural equivalence of learning fuzzy systems and radial basis function networks. In: European Congress on Intelligent Techniques and Soft Computing (EUFIT), pp. 58–66, Aachen, Germany (1994)
Kiendl, H.: Fuzzy-Control methodenorientiert. Oldenbourg, München (1997)
Kortmann, P.: Fuzzy-Modelle zur Systemidentifikation. Reihe 8: Mess-, Steuerungs- und Regelungstechnik, Nr. 647. VDI-Verlag, Düsseldorf (1997)
Kosko, B.: Fuzzy systems as universal approximators. IEEE Trans. Comput. 43, 1329–1333 (1994)
Kroll, A.: Fuzzy-Systeme zur Modellierung und Regelung komplexer technischer Systeme. Reihe 8: Mess-, Steuerungs- und Regelungstechnik, Nr. 612. VDI-Verlag, Düsseldorf (1997)
Kruse, R., Gebhardt, J., Klawonn, F.: Foundations of Fuzzy Systems. John Wiley & Sons, Chichester (1994)
Lee, C.C.: Fuzzy logic in control systems: fuzzy logic controller – part I. IEEE Trans. Syst. Man Cybern. 20(2), 404–418 (1990)
Lee, C.C.: Fuzzy logic in control systems: fuzzy logic controller – part II. IEEE Trans. Syst. Man Cybern. 20(2), 419–435 (1990)
Lindskog, P.: Methods, Algorithms and Tools for System Identification Based on Prior Knowledge. Ph.D. thesis, Linköping University, Linköping, Sweden (1996)
Linkens, D.A., Nyongesa, H.O.: A hierachical multivariable fuzzy controller for learning with genetic algorithms. Int. J. Control 63(5), 865–883 (1996)
Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice Hall, Englewood Cliffs (1999)
Mamdani, E.H.: Application of fuzzy logic to approximate reasoning using linguistic systems. Fuzzy Sets Syst. 26, 1182–1191 (1977)
Mendel, J.M.: Fuzzy logic systems for engineering: a tutorial. Proc. IEEE 83(3), 345–377 (1995)
Nelles, O.: GA-based generation of fuzzy rules. In: Pedrycz, W. (ed.) Fuzzy Evolutionary Computation, chapter 2.9, pp. 269–295. Kluwer Academic Publishers, Boston, USA (1997)
Nelles, O., Ayoubi, M.: Learning the relevance of symtoms in fault trees. In: European Congress on Intelligent Techniques and Soft Computing (EUFIT), pp. 1148–1152, Aachen, Germany (1994)
Nelles, O., Fischer, M., Müller, B.: Fuzzy rule extraction by a genetic algorithm and constrained nonlinear optimization of membership functions. In: International IEEE Conference on Fuzzy Systems (FUZZ-IEEE), pp. 213–219, New Orleans, USA (1996)
Park, D., Kandel, A., Langholz, G.: Genetic-based new fuzzy reasoning models with application to fuzzy control. IEEE Trans. Syst. Man Cybern. 24(1), 39–47 (1994)
Pedrycz, W.: Fuzzy Control and Fuzzy Systems, 2nd edn. John Wiley & Sons, New York (1993)
Pfeiffer, B.-M.: Identification von Fuzzy-Regeln aus Lerndaten. In: Workshop des GMA-UA 1.4.2 “Fuzzy-Control”, pp. 238–250, Dortmund, Germany (1995)
Pfeiffer, B.-M., Isermann, R.: Criteria for successful applications of fuzzy control. Eng. Appl. Artif. Intell. 7(3), 245–253 (1994)
Preuss, H.P.: Fuzzy-Control: Heuristische Regelung mittels unscharfer Logik. Automatisierungstechnik 34(5), 239–246 (1992)
Preuss, H.P., Tresp, V.: Neuro-Fuzzy. Automatisierungstechnische Praxis 36(5), 10–24 (1994)
Raju, G.V.S., Zhou, J.: Adaptive hierarchical fuzzy controller. IEEE Trans. Syst. Man Cybern. 23(4), 973–980 (1993)
Runkler, T.A.: Automatische Selektion signifikanter scharfer Werte in unscharfen regelbasierten Systemen der Informations- und Automatisierungstechnik. Reihe 10, Nr. 417. VDI-Verlag, Düsseldorf (1996)
Setnes, M., Babuška, R., Verbruggen, H.B.: Rule-based modeling: precision and transparency. IEEE Trans. Syst. Man Cybern. Part C 28(1), 165–169 (1998)
Shorten, R., Murray-Smith, R.: Side-effects of normalising basis functions in local model networks. In: Murray-Smith, R., Johansen, T.A. (eds.) Multiple Model Approaches to Modelling and Control, chapter 8, pp. 211–229. Taylor & Francis, London (1997)
Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE Trans. Syst. Man Cybern. 15(1), 116–132 (1985)
Vanderplaats, G.N.: Numerical Optimization Techniques for Engineering Design. Series in Mechanical Engineering. McGraw-Hill, New York (1984)
Wang, L.-X.: Adaptive fuzzy systems and control. design and stability analysis. Prentice Hall, Englewood Cliffs (1994)
Wang, L.-X., Mendel, J.M.: Fuzzy basis functions, universal approximation, and orthogonal least-squares learning. IEEE Trans. Neural Netw. 3(5), 807–814 (1992)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)
Zadeh, L.A.: Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. Syst. Man Cybern. 1, 28–44 (1973)
Zimmermann, H.-J.: Fuzzy Set Theory and its Application, 2nd edn. Kluwer Academic Publishers, Boston (1991)
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Nelles, O. (2020). Fuzzy and Neuro-Fuzzy Models. In: Nonlinear System Identification. Springer, Cham. https://doi.org/10.1007/978-3-030-47439-3_12
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DOI: https://doi.org/10.1007/978-3-030-47439-3_12
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