Fuzzy Representations in Neural Nets

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.

[1]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[2]  W. Silvers.  The Coat Colors of Mice , 1979, Springer New York.

[3]  Roberto Moreno-Díaz,et al.  The fuzzy paradigm for knowledge representation in cerebral dynamics , 1987 .

[4]  Norval F. Pohl.  Scale Considerations in Using Vague Quantifiers. , 1981 .

[5]  Geoffrey E. Hinton,et al.  Distributed Representations , 1986, The Philosophy of Artificial Intelligence.

[6]  Teuvo Kohonen,et al.  Content-addressable memories , 1980 .

[7]  K Y M Wong,et al.  Training noise adaptation in attractor neural networks , 1990 .

[8]  Eric Saund.  Abstraction and Representation of Continuous Variables in Connectionist Networks , 1986, AAAI.

[9]  Aristotle.  The Soul , 1931, Card-Carrying Christians.

[10]  George J. Klir,et al.  Fuzzy sets, uncertainty and information , 1988 .

[11]  Mava Jo Powell.  Purposive vagueness: an evaluative dimension of vague quantifying expressions , 1985 .

[12]  E. Oja.  Simplified neuron model as a principal component analyzer , 1982, Journal of mathematical biology.

[13]  James C. Bezdek,et al.  Pattern Recognition with Fuzzy Objective Function Algorithms , 1981, Advanced Applications in Pattern Recognition.

[14]  Richard P. Lippmann,et al.  An introduction to computing with neural nets , 1987 .

[15]  Isao Hayashi,et al.  NN-driven fuzzy reasoning , 1991, Int. J. Approx. Reason..

[16]  Patrick Bosc,et al.  Fuzzy querying with SQL: extensions and implementation aspects , 1988 .

[17]  Györgyi,et al.  Inference of a rule by a neural network with thermal noise. , 1990, Physical review letters.

[18]  M. Gluck.  Stimulus Generalization and Representation in Adaptive Network Models of Category Learning , 1991 .

[19]  Teuvo Kohonen,et al.  Self-organization and associative memory: 3rd edition , 1989 .

[20]  W. Silvers.  The coat colours of mice. A model for mammalian gene action and interaction. , 1979 .

[21]  D. E. Rumelhart,et al.  Learning internal representations by back-propagating errors , 1986 .

[22]  T Poggio,et al.  Regularization Algorithms for Learning That Are Equivalent to Multilayer Networks , 1990, Science.

[23]  Kurt Hornik,et al.  Neural networks and principal component analysis: Learning from examples without local minima , 1989, Neural Networks.

[24]  D R Shanks,et al.  Connectionism and the Learning of Probabilistic Concepts , 1990, The Quarterly journal of experimental psychology. A, Human experimental psychology.

[25]  Dean A. Pomerleau,et al.  What's hidden in the hidden layers? , 1989 .

[26]  Michael Smithson,et al.  Fuzzy Set Analysis for Behavioral and Social Sciences , 1986 .

[27]  T. Yamakawa.  Stablization of an inverted pendulum by a high-speed fuzzy logic controller hardware system , 1989 .

[28]  Ralph Linsker,et al.  Self-organization in a perceptual network , 1988, Computer.

[29]  Karl H. Pribram,et al.  The Languages of the Brain , 2002 .

[30]  James L. McClelland,et al.  Distributed memory and the representation of general and specific information. , 1985, Journal of experimental psychology. General.

[31]  S W Young,et al.  Visual fuzzy cluster analysis of MR images. , 1989, AJR. American journal of roentgenology.

[32]  Geoffrey E. Hinton,et al.  Symbols Among the Neurons: Details of a Connectionist Inference Architecture , 1985, IJCAI.

[33]  W. Estes,et al.  Base-rate effects in category learning: a comparison of parallel network and memory storage-retrieval models. , 1989, Journal of experimental psychology. Learning, memory, and cognition.

[34]  Anna Wierzbicka,et al.  Precision in vagueness: The semantics of English ‘approximatives’ , 1986 .

[35]  J. Rubner,et al.  A Self-Organizing Network for Principal-Component Analysis , 1989 .

[36]  E. Rosch,et al.  Family resemblances: Studies in the internal structure of categories , 1975, Cognitive Psychology.

[37]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[38]  Elke A. Rundensteiner,et al.  On nearness measures in fuzzy relational data models , 1989, Int. J. Approx. Reason..

[39]  Gail A. Carpenter,et al.  Neural network models for pattern recognition and associative memory , 1989, Neural Networks.

[40]  Bernd Fritzke,et al.  Unsupervised clustering with growing cell structures , 1991, IJCNN-91-Seattle International Joint Conference on Neural Networks.

[41]  H. Zimmermann,et al.  Quantifying vagueness in decision models , 1985 .

[42]  Eliot R. Smith,et al.  Exemplar and Prototype Use in Social Categorization , 1990 .

[43]  D. Medin,et al.  The role of theories in conceptual coherence. , 1985, Psychological review.

[44]  J. MacQueen.  Some methods for classification and analysis of multivariate observations , 1967 .

[45]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[46]  Michael I. Jordan.  An introduction to linear algebra in parallel distributed processing , 1986 .