【作者】 生龙；

【导师】 李春光；

【作者基本信息】 电子科技大学 ， 电路与系统， 2012， 博士

【摘要】 作为对传统模糊集合（一型模糊集合）理论的扩展，1975年Zadeh教授引入了二型模糊集合的概念。二型模糊集合最大的特点就是采用了三维的隶属度函数，使其集合元素的隶属度本身成为一个[0,1]间的模糊数。因此二型模糊集合理论更适用于存在多重不确定性的情况，例如：隶属度函数自身的形状或参数存在不确定性。一型模糊集合理论是传统集合理论的扩展，当一个元素不能完全属于或完全不属于某个集合时（即其属于某个集合的“程度”介于0与1之间时）我们选择一型模糊集合。进一步的，当一个元素属于某个集合的“程度”也不确定时（即该元素属于某个集合的隶属度值也不确定时），我们就可以选择二型模糊集合。模糊集合理论的应用大部分都集中在模糊系统上。模糊系统是以模糊集合理论为基础的一种基于知识或规则的系统，其核心是由IF-THEN规则组成的知识库。二型模糊系统与传统的一型模糊系统相类似，也是通过组合IF-THEN规则构造而成。但因为其理论基础为二型模糊集合理论，所以二型模糊系统较一型模糊系统而言，可以直接掌控更多的不确定性信息。由于二型模糊集合的运算复杂度较高，目前大多数基于二型模糊集合理论的应用都选择采用区间二型模糊集合。本论文通过构建区间二型模糊系统模型，着重研究了二型模糊系统理论在自动化控制领域和模式识别领域的应用。主要内容为：1．构建了离散区间二型T-S模糊系统模型，采用并行分布式补偿法设计出了针对该模型的模糊控制系统。利用李亚普诺夫方法，以线性矩阵不等式的形式给出了该系统稳定工作的约束条件，并用数值仿真验证了该约束条件的有效性。通过颠簸路面上自主平行泊车控制系统的应用实例，详细介绍了该离散二型T-S模糊控制系统的设计过程，验证了二型模糊系统在掌控多重不确定性信息方面的优势。2．基于具有时延特性的连续区间二型T-S模糊系统模型，采用并行分布式补偿法设计出相应的模糊控制系统。利用李亚普诺夫方法，以线性矩阵不等式的形式给出了系统稳定工作的约束条件，并用数值仿真验证了该控制系统的有效性。以连续搅拌槽反应过程控制为例，详细介绍了具有时延特性的连续区间二型T-S模糊控制系统的设计过程，并进一步验证了二型模糊系统在掌控多重不确定信息方面较一型模糊系统所具有的优势。3．针对中文自动摘要问题，提出了一种基于二型模糊C均值聚类算法的摘要自动提取方案。该方案以中文句子为单位，通过计算中心句特征、标题特征、高频词特征、首句特征、句子长度、句子位置、数量词特征构建特征向量，对文本内容进行聚类分析，找出文本内容中的关键句来构建摘要。最后通过与采用一型模糊C均值算法的自动摘要结果相对比，验证了基于二型模糊集合的摘要算法比基于一型模糊集合的摘要算法获得的摘要结果更准确。4．针对数字音频信号分类问题，提出了基于二型模糊集合理论的C均值聚类算法，在此基础上应用跳跃基因遗传算法对聚类得到的初始模糊模型进行优化，并采用向量相似性测度准则对优化后的模糊规则进行简化，得到最终的模糊分类器模型。通过实例仿真验证了采用二型模糊C均值聚类算法的音频信号分类器比采用一型模糊C均值聚类算法的分类器得到的分类结果更准确。更多还原

【Abstract】 In1975, Professor Zadeh introduced the type-2fuzzy set to expand the traditionalfuzzy set (type-1fuzzy set). Compared with the type-1fuzzy set, the most advantage ofthe type-2fuzzy set is to use three-dimensional membership functions, so themembership degree of the element becomes a fuzzy number in [01]. The type-2fuzzysets theory is more applicable to the case of the multi-uncertainty. For example, theshape or parameters of membership functions are uncertain. When an element can notbe entirely part of a set (the membership of the element that belongs to a set is between0and1), we choose type-1fuzzy sets. When the “membership” of an element belongsto a set is uncertain (the membership degree of an element is uncertain), we can choosethe type-2fuzzy sets.Now, fuzzy systems have become most successful in the applications of fuzzy setstheory. The core of a fuzzy system is the knowledge database formed by fuzzyIF-THEN rules, which is based on the fuzzy sets theory. The same as the type-1fuzzysystem, type-2fuzzy system is also constructed by the combination of fuzzy IF-THENrules. However, the type-2fuzzy system is based on type-2fuzzy sets. Compared withthe type-1fuzzy system, the type-2fuzzy system can handle the multi-uncertaintydirectly. Because the high computational complexity of the type-2fuzzy sets, most ofthe applications of type-2fuzzy sets theory focus on the interval type-2fuzzy sets.Through constructing the model of interval type-2fuzzy systems, this PhD thesisstudies the applications of type-2fuzzy system in the field of automatic control andpattern recognition. The main contents are as follows:1. Based on the discrete interval type-2T-S fuzzy model, a fuzzy control system isdesigned by using the parallel distributed compensation. By using the Lyapunovmethod, the stabilization of the control system is analyzed, and the results arepresented in terms of linear matrix inequalities. The effectiveness of the resultsis illustrated by numerical simulations. Finally, the type-2fuzzy controllerdesign for autonomous parallel parking on bumpy road is applied to detail the design processes. The simulation results have showed the advantages of type-2fuzzy control systems on handling the information of multi-uncertainty.2. Based on the continued interval type-2T-S fuzzy model with time-varing delay,a fuzzy control system is designed by using the parallel distributedcompensation. By using the Lyapunov method, the stabilization of the controlsystem is analyzed, the results are presented in terms of linear matrixinequalities. The effectiveness of the control system is verified by numericalsimulations. Finally, the type-2fuzzy controller design for the continuous stirredtank reactor is discussed to detail the design process. The results of thesimulations further illustrate the advantages of type-2fuzzy control systems onhandling the information of multi-uncertainty.3. Chinese automatic summarization method is discussed based on the type-2fuzzy C-means clustering. In order to use the cluster analysis method, it isnecessary to represent Chinese sentences as vectors of features. These featuresinclude sentence centrality, title feature, high frequency words feature, firstsentence feature, sentence length, sentence position, and numerical data feature.Based on the text clustering analysis, the key sentences of the text can be foundout to construct the summary. Finally, the experiments have showed that theChinese automatic summarization result is more accurate to adopt the type-2fuzzy system than to adopt the type-1fuzzy system.4. Type-2fuzzy c-means clustering algorithm is applied to solve the digital audiosignal classification problem, and jumping genes genetic algorithm is used tooptimize the initial fuzzy model which is obtained by the clustering algorithm.At last, the optimized fuzzy rule base is simplified by the vector similaritymeasure, and the final fuzzy classifier model is obtained. Compared to theconventional type-1fuzzy sets, type-2fuzzy sets can handle more uncertaininformation. Especially for sample sets whose samples distribute uneven andstructures are irregular. The experiment results are more precise when the type-2fuzzy c-means clustering algorithm is adopted.更多还原