Theory And Application Of Additive-Multiplicative Fuzzy Neural Networks

From the view of knowledge processing, fuzzy systems and neural networks can be systematically studied in the light of representation vs. structure, reasoning vs. computation, and acquisition vs. learning. From the view of function approximation, fuzzy systems and neural networks can be studied in view of equivalence in the sense of universal function approximation. In this thesis, the probability and practicability of combining the fuzzy logic systems with the neural networks are studied with the insight of the two views, namely, the view of knowledge processing and the view of function approximation.The domestic and international achievement about this field was investigated, analyzed and referenced to propose Additive-Multiplicative Fuzzy Neural Network (AMFNN). Theoretical structure and practice applications of this new fuzzy neural network have been systematically, theoretically and deeply analyzed and researched, and the following achievements are obtained:1. The thesis presented a model of Additive-Multiplicative Fuzzy Neural Networks and the model's structure as well. In the thesis, it is proved that this fuzzy neural networks can approximat at any degree of accuracy to any real continuous function in a compact domain by means of Stone-Weirstrass Law. Error Back Propagation algorithm for the model of Additive-Multiplicative Fuzzy Neural Networks is presented according to the Gradient Descent Method in the thesis, along with the study of the model's application to fuzzy reasoning.2. Based on the achievement, Relationship Clustering Algorithm is proposed to obtain fuzzy rules effectively.3. Based on generalized Gaussian function, Additive-Multiplicative Fuzzy Neural Networks has been generalized reasonably and Generalized Additive-Multiplicative Fuzzy Neural Networks has been proposed. The architecture and learning algorithm of Generalized Additive-Multiplicative Fuzzy Neural Networks has been deeply researched. The matrix coding in genetic algorithm (GA), which combines binary coding and real number coding, is adopted to searchthe optimal parameters of the generalized AMFNN and determine the number of fuzzy rules. The generalized AMFNN has lower complexity and can approximate to a nonlinear system at high accuracy degree. Numerical simulations have demonstrated the validity of this approach.4. Based on assigning a conditional probability factor (p(B|A)) to each if-then fuzzy rule (e.g. A-B), Additive-Multiplicative Fuzzy Neural Networks with probability factor has been presented. In this fuzzy model, the probability factor of each rule is interpreted as a fuzzy conditional probability of rule consequent given rule antecedent. The universal approximation of this model has been proved. The method and process of obtaining the fuzzy if-then rules and conditional probability also has been research based on the former achievement. The probability factor obtaining method based on Fuzzy Naive Bayes Classifier is also discussed. The simulation results show that the prediction performance of the fuzzy inference model with fuzzy probability factor is always better than the fuzzy inference model without t fuzzy probability factor.5. The fuzzy rules acquisition and optimal selection of fuzzy rules is concerned in this paper. Based on the former achievement, two optimal selection methods, two-stage clustering algorithm and optimal selection method based on rough sets, have been studied.6. For testing the performance of Additive-Multiplicative Fuzzy Neural Networks in practice, it has been put into engineering practices, such as model identifying, fuzzy control, noise canceling, congestion control in ATM network, stability analysis of unloading rock, safety factor calculation of rock mass slope.In addition, the Turbo C code realization programs of the foregoing fuzzy neural networks are provided and are all proved to be effective by experimenting with practical data, separately.