Abstract
Clear, crisp, precise and unambiguous: that is how you like your concepts, if you are a serial computer. But human concepts are in general vague, fuzzy or subject to borderline cases. Anyone who deals with information via computers knows the problems arising from having to categorise objects to fit the computer's crude pigeonholes, and how inflexible this is compared to what humans do. Conversely, those of us who teach mathematics and related subjects know how hard it is to induce the brain to represent clear and precise concepts.
Preview
Unable to display preview. Download preview PDF.
References
Aristotle: On the Soul. (350 BC).
Baldi, P. Hornik, K.: Neural networks and principal component analysis. Neural Networks 2: (1989) 53–58.
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms Plenum, New York, (1981).
Bosc, P., Galibourg, M., Hamon, G.: Fuzzy querying with SQL: extensions and implementation aspects. Fuzzy Sets and Systems 28: (1988) 333–349.
Carpenter, G.A.: Neural network models for pattern recognition and associative memory. Neural Networks 2: (1989) 243–257.
Cybenko, G.: Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals and Systems 2: (1989) 303–314.
Estes, W.K., Campbell, J.A., Hatsopoulos, N., Hurwitz, J.B.: Base-rate effects in category learning: a composition of parallel network and memory storage-retrieval models. Journal of Experimental Psychology: Learning, Memory & Cognition 15: (1989) 556–571.
Fritzke, B.: Unsupervised clustering with growing cell structures. Proceedings of the IJCNN-91, Seattle, (1991).
Funahashi, K.-I.: On the approximate realization of continuous mappings by neural networks. 0 Neural Networks 2: (1989) 183–192.
Gluck, M.A.: Stimulus generalization and representation in adaptive network models of category learning. Psychological Science 2: (1991) 50–55.
Györgyi, G.: Inference of a rule by a neural network with thermal noise. Physical Review Letters 64: (1990) 2957–2960.
Hayes, B.K., Taplin, J.E.: The effects of existing knowledge on the learning of artificial categories. in: (A.F. Bennett & K.M. McConkey, eds), Cognition in Individual and Social Contexts North-Holland, (1989).
Herz, A., Sulzer, B., Kühn R., van Hemmen, J.L.: Hebbian learning reconsidered: representation of static and dynamic objects in associative neural nets. Biological Cybernetics 60: (1989) 457–467.
Hinton, G.E., McClelland, J.L., Rumelhart, D.E.: Distributed representations. Chapter 3 of D.E. Rumelhart & J.L. McClelland, Parallel Distributed Processing, MIT Press, 1986.
Jordan, M.I.: An introduction to linear algebra in parallel distributed processing. Chapter 9 of D.E. Rumelhart & J.L. McClelland, Parallel Distributed Processing, MIT Press, 1986.
Kamgar-Parsi, B., Gualtieri, J.A., Devaney, J.E., Kamgar-Parsi, B.: Clustering with neural networks. Biological Cybernetics 63: (1990) 201–208.
Klir, G., Folger, T.: Fuzzy Sets, Uncertainty and Information, Prentice-Hall, (1988).
Kohonen, T.: Content Addressable Memories. Springer Verlag, (1980).
Kohonen, T.: Self-Organization and Associative Memory 3rd edition, Springer Verlag, (1989).
Kosko, B.: Neural Networks and Fuzzy Systems. Prentice Hall, 1991.
Lee, C.C. Fuzzy logic in control systems', IEEE Trans. on Systems, Man and Cybernetics 20: 404–418 (part 1), 419–435 (part 2) (1990).
Lippmann, R.P.: An introduction to computing with neural nets. IEEE ASSP Magazine 4(4): 4–22, (1987).
Linsker, R. Self-organization in a perceptual network. Computer 21(3): (1988) 105–117.
MacQueen, J.: Some methods for classification and analysis of multivariate observations. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability vol I pp. 281–297, (1967).
McClelland, J.L., Rumelhart, D.E. Distributed memory and the representation of general and specific information. Journal of Experimental Psychology: General 114: (1985) 159–188.
Mira, J., Delgado, A.E., Moreno-Dìz: The fuzzy paradigm for knowledge representation in cerebral dynamics. Fuzzy Sets and Systems 23: (1987) 315–330.
Murphy, G.L., Medin, D.L.: The role of theories in conceptual coherence. Psychological Review 92: (1985) 289–316.
Oja, E.: A simplified neuron model as a principal component analyzer. Journal of Mathematical Biology 15: (1982) 267–273.
Pao, Y.-H.: Adaptive Pattern Recognition and Neural Networks Addison-Wesley, (1989).
Poggio, T., Girosi, F.: Regularization algorithms for learning that are equivalent to multilayer networks. Science 247: 978–982 (1990).
Pohl, N.F.: Scale considerations in using vague quantifiers. Journal of Experimental Education 49: (1980) 235–240.
Powell, M.J.: Purposive vagueness. Journal of Linguistics 21: (1985) 31–50.
Pribram, K.H.: Languages of the Brain. Prentice Hall, (1971).
Rosch, E., Mervis, C.B.: Family resemblances: studies in the internal structure of categories. Cognitive Psychology 7: (1975) 573–605.
Rubner, J., Taran, P.: A self-organizing network for principal-component analysis. Europhysics Letters 10: (1989) 693–698.
Rumelhart, D.E., Hinton, G.E., Williams, R.J.: Learning internal representations by back-propagating errors. Nature 323: (1986), 533–536.
Rundensteiner, E.A., Hawkes, L.W., Bandler, W.: On nearness measures in fuzzy relational data models. International Journal of Approximate Reasoning 3: (1989) 267–298.
Saund, E.: Abstraction and representation of continuous variables in connectionist networks. in: Proceedings AAAI-86, Philadelphia: (1986) 638–644.
Shanks, D.R.: Connectionism and the learning of probabilistic concepts. Quarterly Journal of Experimental Psychology 42A: (1990) 209–237.
Silvers, W.K.: The Coat Colours of Mice: A Model for Mammalian Gene Action and Interaction, Springer Verlag, (1979).
Smith, E.R., Zarate, M.A.: Examplar and prototype use in social categorization. Social Cognition 8: (1990) 243–262.
Smithson, M.: Fuzzy Set Analysis for Behavioural and Social Sciences, Springer Verlag, (1987).
Takagi, H., Hayashi, I.: NN-driven fuzzy reasoning. International Jopurnal of Approximate Reasoning 5: (1991) 191–212.
Touretzky, D.S., Hinton, G.E.: Symbols among the neurons. Proceedings of 9th International Joint Conference on Artificial Intelligence Vol. 1: (1985) 238–243.
Touretzky, D.S., Pomerleau, D.A.: What's hidden in the hidden layers. Byte (Aug): (1989) 227–233.
Wierzbicka, A.: Precision in vagueness: the semantics of English approximatives. Journal of Pragmatics 10: (1986) 597–614.
Wong, K.Y.M., Sherrington, D.: Training noise adaptation in attractor neural networks. Journal of Physics and Applied Math. Gen. 23: (1990) L175–L182.
Yamakawa, T.: Stabilization of an inverted pendulum by a high-speed fuzzy logic controller hardware system. Fuzzy Sets and Systems 32: (1989) 161–180.
Young. S.W., Ballerio, C., Carrol, C.L.: Visual fuzzy cluster-analysis of MR images. American Journal of Roentgenology 152: (1989) 19–25.
Zimmermann, H.-J., Zysno, P.: Quantifying vagueness in decision models. European Journal of Operational Research 22: (1985) 148–158.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Franklin, J. (1994). Fuzzy representations in neural nets. In: Driankov, D., Eklund, P.W., Ralescu, A.L. (eds) Fuzzy Logic and Fuzzy Control. IJCAI 1991. Lecture Notes in Computer Science, vol 833. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58279-7_20
Download citation
DOI: https://doi.org/10.1007/3-540-58279-7_20
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-58279-3
Online ISBN: 978-3-540-48602-2
eBook Packages: Springer Book Archive