Neural Networks and Fuzzy Systems - A Dynamical Systems by Bart Kosko

By Bart Kosko

Combining neural networks and fuzzy structures, this provides neural networks as trainable dynamical platforms and develops mechanisms and rules of adaption, self-organization, covergence and international balance. it is also the recent geometric conception of fuzzy units, platforms and associative thoughts. Kosko indicates the best way to practice fuzzy idea to adaptive regulate and the way to generate based fuzzy structures with unsupervised neural ideas. The booklet is designed to be acceptable for classes in engineering, laptop technological know-how, arithmetic, psychology and biology.

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The dimensionality of the state space also docs not in principle affect the convergence rate. In practice, CJ converges exponentially quickly. This suggests that global stability may under! ic our biological neural net works· ability to rapidly recognize patterns. generate 16 NEURAL NETWORKS AND FUZZY SYSTEMS CHAP. 3 Global stability of a feedback neural network. Learning encodes the vector patterns P 1 , P2 , ••• by gradually sculpting a Lyapunov or "energy" surface in the augmented state space R"+ 1• Input vector pattern Q rapidly "rolls" into the nearest attractor basin, where the system classifies Q as a learned pattern P or misclassifies Q as a spurious pattern.

The 2" vertices of /" represent extremized neuronal-output combinations, as we often find in networks of competitive or laterally inhibitive neurons. Many feedback neural networks [Hopfield, 1984] drive initial states inside the unit cube to nearest vertices. These systems dynamically disambiguate fuzzy input descriptions by minimizing their fuzzy entropy. The midpoint of the cube, where a fuzzy set A equals its own opposite "1'. has maximal fuzzy entropy, as we discuss in Chapter 7. The black-white ve11ices have minimal fuzzy entropy.

They "learn from experience" with numerical and, sometimes, linguistic sample data. Neural and fuzzy systems encode sampled information in a parallel-distributed framework. Both frameworks are numerical. We can prove theorems to describe their behavior and limitations. We can implement neural and fuzzy systems in digital or analog VLSI circuitry or in optical-computing media, in spatial-light modulators and holograms. Artificial neural networks consist of numerous, simple processing units or "neurons" that we can globally program for computation.

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