Top Document: comp.ai.neuralnets FAQ, Part 7 of 7: Hardware Previous Document: What about Genetic Algorithms? Next Document: Unanswered FAQs See reader questions & answers on this topic!  Help others by sharing your knowledge Fuzzy logic is an area of research based on the work of L.A. Zadeh. It is a departure from classical twovalued sets and logic, that uses "soft" linguistic (e.g. large, hot, tall) system variables and a continuous range of truth values in the interval [0,1], rather than strict binary (True or False) decisions and assignments. Fuzzy logic is used where a system is difficult to model exactly (but an inexact model is available), is controlled by a human operator or expert, or where ambiguity or vagueness is common. A typical fuzzy system consists of a rule base, membership functions, and an inference procedure. Most fuzzy logic discussion takes place in the newsgroup comp.ai.fuzzy (where there is a fuzzy logic FAQ) but there is also some work (and discussion) about combining fuzzy logic with neural network approaches in comp.ai.neuralnets. Early work combining neural nets and fuzzy methods used competitive networks to generate rules for fuzzy systems (Kosko 1992). This approach is sort of a crude version of bidirectional counterpropagation (HechtNielsen 1990) and suffers from the same deficiencies. More recent work (Brown and Harris 1994; Kosko 1997) has been based on the realization that a fuzzy system is a nonlinear mapping from an input space to an output space that can be parameterized in various ways and therefore can be adapted to data using the usual neural training methods (see "What is backprop?") or conventional numerical optimization algorithms (see "What are conjugate gradients, LevenbergMarquardt, etc.?"). A neural net can incorporate fuzziness in various ways: o The inputs can be fuzzy. Any gardenvariety backprop net is fuzzy in this sense, and it seems rather silly to call a net "fuzzy" solely on this basis, although Fuzzy ART (Carpenter and Grossberg 1996) has no other fuzzy characteristics. o The outputs can be fuzzy. Again, any gardenvariety backprop net is fuzzy in this sense. But competitive learning nets ordinarily produce crisp outputs, so for competitive learning methods, having fuzzy output is a meaningful distinction. For example, fuzzy cmeans clustering (Bezdek 1981) is meaningfully different from (crisp) kmeans. Fuzzy ART does not have fuzzy outputs. o The net can be interpretable as an adaptive fuzzy system. For example, Gaussian RBF nets and Bspline regression models (Dierckx 1995, van Rijckevorsal 1988) are fuzzy systems with adaptive weights (Brown and Harris 1994) and can legitimately be called neurofuzzy systems. o The net can be a conventional NN architecture that operates on fuzzy numbers instead of real numbers (Lippe, Feuring and Mischke 1995). o Fuzzy constraints can provide external knowledge (Lampinen and Selonen 1996). More information on neurofuzzy systems is available online: o The Fuzzy Logic and Neurofuzzy Resources page of the Image, Speech and Intelligent Systems (ISIS) research group at the University of Southampton, Southampton, Hampshire, UK: http://wwwisis.ecs.soton.ac.uk/research/nfinfo/fuzzy.html. o The NeuroFuzzy Systems Research Group's web page at Tampere University of Technology, Tampere, Finland: http://www.cs.tut.fi/~tpo/group.html and http://dmiwww.cs.tut.fi/nfs/Welcome_uk.html o Marcello Chiaberge's NeuroFuzzy page at http://polimage.polito.it/~marcello. o The homepage of the research group on Neural Networks and Fuzzy Systems at the Institute of Knowledge Processing and Language Engineering, Faculty of Computer Science, University of Magdeburg, Germany, at http://www.neurofuzzy.de/ o JyhShing Roger Jang's home page at http://www.cs.nthu.edu.tw/~jang/ with information on ANFIS (Adaptive NeuroFuzzy Inference Systems), articles on neurofuzzy systems, and more links. o Andrew Gray's Hybrid Systems FAQ at the University of Otago at http://divcom.otago.ac.nz:800/COM/INFOSCI/SMRL/people/andrew/publications/faq/hybrid/hybrid.htm References: Bezdek, J.C. (1981), Pattern Recognition with Fuzzy Objective Function Algorithms, New York: Plenum Press. Bezdek, J.C. & Pal, S.K., eds. (1992), Fuzzy Models for Pattern Recognition, New York: IEEE Press. Brown, M., and Harris, C. (1994), Neurofuzzy Adaptive Modelling and Control, NY: Prentice Hall. Carpenter, G.A. and Grossberg, S. (1996), "Learning, Categorization, Rule Formation, and Prediction by Fuzzy Neural Networks," in Chen, C.H. (1996), pp. 1.31.45. Chen, C.H., ed. (1996) Fuzzy Logic and Neural Network Handbook, NY: McGrawHill, ISBN 0070111898. Dierckx, P. (1995), Curve and Surface Fitting with Splines, Oxford: Clarendon Press. HechtNielsen, R. (1990), Neurocomputing, Reading, MA: AddisonWesley. Klir, G.J. and Folger, T.A.(1988), Fuzzy Sets, Uncertainty, and Information, Englewood Cliffs, N.J.: PrenticeHall. Kosko, B.(1992), Neural Networks and Fuzzy Systems, Englewood Cliffs, N.J.: PrenticeHall. Kosko, B. (1997), Fuzzy Engineering, NY: Prentice Hall. Lampinen, J and Selonen, A. (1996), "Using Background Knowledge for Regularization of Multilayer Perceptron Learning", Submitted to International Conference on Artificial Neural Networks, ICANN'96, Bochum, Germany. Lippe, W.M., Feuring, Th. and Mischke, L. (1995), "Supervised learning in fuzzy neural networks," Institutsbericht Angewandte Mathematik und Informatik, WWU Muenster, I12, http://wwwmath.unimuenster.de/~feuring/WWW_literatur/bericht12_95.ps.gz Nauck, D., Klawonn, F., and Kruse, R. (1997), Foundations of NeuroFuzzy Systems, Chichester: Wiley, ISBN 0471971510. van Rijckevorsal, J.L.A. (1988), "Fuzzy coding and Bsplines," in van Rijckevorsal, J.L.A., and de Leeuw, J., eds., Component and Correspondence Analysis, Chichester: John Wiley & Sons, pp. 3354. User Contributions:Comment about this article, ask questions, or add new information about this topic:Top Document: comp.ai.neuralnets FAQ, Part 7 of 7: Hardware Previous Document: What about Genetic Algorithms? 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Last Update March 27 2014 @ 02:11 PM
