【作者】 张持健；

【导师】 张铃；

【作者基本信息】 安徽大学 ， 计算机应用技术， 2005， 博士

【摘要】 Zadeh在1965年提出“fuzzy sets”后,奠定了模糊逻辑的第一块基石。四十年来模糊逻辑和模糊控制系统的理论与应用都得到了迅速的发展,也取得了令人瞩目的成果。但是由于对其缺乏系统的理论分析与设计方法的研究,模糊逻辑和模糊控制如何取得成功?什么是它的本质属性?如何将新型神经网络应用到模糊逻辑中并构造一个具有自适应以及良好泛化能力的模糊逻辑系统?如何在高维数和高精度的模糊控制系统中全面解决模糊逻辑的“规则爆炸”问题及提出相应的理论框架?所有这些问题使得有必要对其进行更深入研究。 商空间理论作为一种问题求解的方法,其坚实的理论基础,多侧面、多角度的问题求解方法,是解决问题时缩小求解难度,降低计算量的强有力工具。利用问题求解的商空间理论把定性的思维和定量的分析有机地统一起来,本文分析、处理了模糊逻辑工程所要解决的模糊逻辑本质问题和结构优化问题。把商空间理论应用到模糊逻辑的研究,将是一个具有广泛应用前景的课题。本文主要工作如下: 1.回顾了计算智能在模糊逻辑中的研究进展和应用,讨论了商空间理论在模糊逻辑工程领域研究和应用的依据和意义。通过将商空间理论应用于模糊逻辑的本质和鲁棒性行为的研究,提出了序关系结构是模糊控制系统成功的基础(必要条件),基于模糊等价关系的分层递阶结构保证了模糊控制系统的结构鲁棒性(性能鲁棒性和稳定鲁棒性)。在模糊控制系统中,模糊隶属度函数的区别并不是主要的,关键是他们的分层递阶结构是否相同。这些结论克服了人们在模糊控制系统隶属度函数定义上的主观性,澄清人们对模糊集理论和模糊控制的疑虑,使之建立在更为客观的理论基础上。在一定程度上解决了模糊控制系统设计中长期困扰人们的模糊隶属度函数的取值问题。从而为模糊逻辑和模糊控制技术的进一步发展奠定了基础。MATLAB实验证明以上结论正确。 2.在分析模糊控制系统设计现状的基础上(特别是模糊自适应神经网络),提出了基于FP神经网络覆盖算法的模糊系统设计。首先改进了原有的FP覆盖算法,在此基础上利用前面提出的模糊集的结构性定义,建立了模糊FP神经网络覆盖算法的理论框架和系统。通过引用模糊集结构性定义的思想,充分利用了更多还原

【Abstract】 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.更多还原