| Neural networks and fuzzy systems, both of which can imitate human intelligent behavior, are two kinds of main intellectual technologies with their own characteristics. Fuzzy systems are good at exploiting human experienced knowledge. However, it is very difficult to identify the fuzzy rules and tune the membership functions automatically, which hinders the further popularization of fuzzy information processing technology. On the other hand, neural networks have adaptive learning ability, but they can not use priori knowledge to learn, and their structure is difficult to understand since their knowledge is expressed as a "black box"Based on further research on neural networks and fuzzy systems, many researchers inte-grate them into a unified framework called fuzzy neural networks (FNNs). On the one hand, by introducing fuzzy technology into neural networks one can widen the range of processing information for, and improve the capability of, neural networks. FNNs can thus realize fuzzy association and fuzzy mapping. On the other hand, it becomes possible to identify the fuzzy rules and tune the membership functions automatically by using neural networks to deal with fuzzy information. Fuzzy neural networks possess not only the learning and optimizing abili-ties and the hierarchical structure of neural networks, but also the fuzzy "if-then" rules of fuzzy systems. And it is easy to be embedded into expert knowledge and to be understood.There is relatively few theoretical analysis of fuzzy neural networks, even though it has been successfully applied in intelligent control, pattern recognition and system identification, etc. Therefore, it is meaningful to analyze the learning ability and convergence of neuro-fuzzy learning algorithms. In this dissertation, the learning algorithms and convergence of these al-gorithms for fuzzy neural networks are studied. As intuitionistic fuzzy sets are more expressive than fuzzy sets when dealing with uncertain information, some primary discussion on the com-bination of intuitionistic fuzzy sets and neural networks is made as well. The organization of this dissertation is as follows:Some background information on conventional neural networks and fuzzy neural networks is reviewed in Chapter 1.The second chapter considers a fuzzy perceptron, of which the inner operations involved in the working process are based on the max-min logical operations rather than conventional multiplication and summation. A learning algorithm based on a fuzzyδrule is proposed for this fuzzy perceptron. The learning algorithm has an advantage, as is proved, that it converges in finite steps if the training patterns are fuzzily separable. This result generalizes a corresponding classical result for conventional linear perceptron.A fuzzy neural network based on zero-order Takagi-Sugeno inference systems is consid-ered in Chapter 3. An improved gradient-based neuro-fuzzy learning algorithm is proposed. This improved algorithm, compared with conventional gradient-based neuro-fuzzy learning al-gorithm, reduces the cost of calculating the gradient of the error function and improves the learning efficiency. The monotonicity of the error function and some weak and strong conver-gence results for this algorithm are proved. Some numerical examples are provided to support the theoretical findings.Intuitionistic fuzzy sets (IFSs) are generalization of fuzzy sets by adding an additional at-tribute parameter called non-membership degree. In Chapter 4, a max-min intuitionistic fuzzy Hopfield neural network (IFHNN) is proposed by combining IFSs with Hopfield neural net-works. The stability of IFHNN is also investigated.In Chapter 5, an intuitionistic fuzzy associative memory (IFAM) network is proposed by combining IFSs with associative memory network. Based on Godel fuzzy implication operator and its dual fuzzy coimplication operator, a learning rule for multiple intuitionistic fuzzy pattern pairs in IFAM is presented. The storage capacity of IFAM is also investigated.
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