Convergence For A Fuzzy Perceptron With Bias

The rapid development of modern technologies makes the the control theory develop much quickly. Fuzzy control and neural networks (NN) are attracting much attention. Fuzzy system is good at knowledge-expressing while it depends on the man' s subjective factors. NN is specialized in self-organizing and self-learning, but its network parameters lack physical meaning and it easily traps into the local minimum.Fuzzy neural networks (FNN) is an organic integration of fuzzy theory and NN, which is self-adaptive and associative, and can carry out fuzzy reasoning. FNN is formed by fuzzy neurons through certain rules. Their theories, structures and algorithms get lots of attachment for their advantages. In this dissertation, the following aspects of FNN are discussed:1. The research status and application fields are reviewed. The basic definitions, structures and learning algorithms of fuzzy theories of NNs and FNN are introduced. The advantages and disadvantages of fuzzy systems and NNs are analyzed and compared.2. NNs are good at information processing and is widely applied to solve classification problems. The capability of solving classification problems for a fuzzy per-ceptron is discussed in this dissertation. A modified algorithm for a fuzzy perceptron with bias is presented. In the case that the fuzzy training patterns are separable, if the dimension of training patterns is 2, the algorithm is finite convergent;and if the dimension of training patterns is greater than 2, the algorithm is finite convergent under some stronger conditions.3. Five training pattern groups are classified using fuzzy perceptron with and without bias, respectively. The experimental results show that the algorithm of a fuzzy perceptron with bias is finite convergent, and the convergence speed is quicker compared with the one without bias under the same experiment condition. This illuminates that the fuzzy perceptron with bias is applicable to save the training time.