Problem Solving Of Fuzzy System & Fuzzy Control Based On The Theory Of Quotient Space

Fuzzy set, proposed by Zadeh in 1965, laid the foundation for fuzzy logic. During the following 40 years, theories and applications of fuzzy set and system has made great progress and obtained highlighted achievement. However, there are, lacking of systematical design and theoretical analysis, a lot of issues to be further studied. How do fuzzy logic and fuzzy control get their success? What are their essential properties? How to, by applying new neural network to fuzzy logic, design self-adaptive fuzzy logic system with well performance? How to overcome the difficulty resulted from "rule explosion" of fuzzy control system with high precision or multi-dimension and to present general theoretical framework of this question? All these problems make it necessary to further investigate in this field.As a method of problem solving, quotient space theory, based on substantial theory, considering the problem from different aspects and multi-hierarchy in the process of problem solving, is a kind of powerful tool in that it can decrease the difficulty of the problem and reduce the computational cost. Unifying the quantitative analysis and the qualitative analysis by utilizing quotient space theory, the thesis analyze and answer the problem of essence of fuzzy logic and the optimization of the control structure. It will be an issue with extensively applicable prospects. Main works and result of thesis include:1. Computational intelligence research process and application in the fuzzy logic are reviewed, and the foundation and significance of applying quotient space theory to the field of fuzzy logic engineering is also discussed. Using the theory of quotient space into research of essence and robustness of fuzzy control, it is proposed that the order relation is the foundation of success of fuzzy control and the hierarchical structure based on the fuzzy equivalence relation ensures the robustness of control system. In the fuzzy control system, we draw a conclusion that the key is the hierarchical structure between elements of universe of discourse, and especially the order relation of them, not the membership function. This conquers the man's subjectivity of the definition of membership functions of fuzzy control and makes it more objective. In some sense, we solve the problem, which confused people for a long time, of how to get the value of membership functions in design of fuzzy control system. Matlab's simulation demonstrates the above-mentioned conclusions.2. After analyzing status of the design fuzzy control system (especially fuzzyself-adaptive NN), the thesis presents the method (F-CSN), which is based on NN spherical covering algorithm (CSN), of designing fuzzy system. The theoretical framework, founding on the improved CSN and structural definition of fuzzy set, is constructed. This method, utilizing the idea of structural definition of fuzzy set, making the best of relational information among samples together with information between samples and kernel sets, can give reasonable setting of boundary of fuzzy pattern classification. Improved methods of FCSN, such as the adjustment of kernel, covering radius, superpose linearity or square of sample density, are used to finely adjust the boundary of fuzzy classifier. The experiments show that using F-CSN can get good result. In the same time, by the use of special result of three top of F-CSN, the thesis presents the ensemble methods of F-CSN (FCSN-EN). Through the ensemble methods of simple vote, superpose the membership function or fixed weight, we can get satisfactory results compared with Internet's. The improved methods of the FCSN-EN, such as how to kill the worse FCSN and improve the ensemble result by others, how to realize the FCSN-EN based on synthesize of fuzzy relation, is exploited to get high precision and generalization. Theoretical analysis of algorithm, experiment with UCI repository and the analysis of experiment result are also given.3. The granularity principles of quotient space theory are applied to the optimization of machine learning. The reduction of rules of fuzzy control system is realized on the base of hierarchical method of quotient space theory. As to the problem of "rule explosion" generated by multi-dimension and high precision, the thesis presents complexity analysis based on hierarchical problem solving. Theory, algorithm and optimal result of the reduction of rules are also proposed. The validity of the above-mentioned method is demonstrated by a high precision fuzzy control system.