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Alternative TitleComputing with Words and Linguistic Dynamic System Research based on Interval Type-2 Fuzzy Method
Thesis Advisor王飞跃
Degree Grantor中国科学院研究生院
Place of Conferral中国科学院自动化研究所
Degree Discipline控制理论与控制工程
Keyword区间二型模糊方法 I型词计算 Ii型词计算 I型语言动力学系统 Ii型语言动力学系统 胞空间方法 Interval Type-2 Fuzzy Method Type-i Computing With Words Type-ii Computing With Words Type-i Linguistic Dynamic Systems Type-ii Linguistic Dynamic Systems Cell Space Method
Abstract常规动力学系统是研究物理工程系统有效的方法,在促进现代科学技术发展和改善人民生活方面都取得很多成果。但是,随着人们的研究领域从工程系统延伸到社会系统时,传统的常规动力学系统的局限性就暴露出来。利用基于精确数学模型的常规动力学系统来研究经济和管理等复杂系统是不可行的。为了有效的解决经济和管理等复杂系统的分析、预测和综合问题,本文提出基于词计算的语言动力学系统来分析和研究经济和管理等复杂系统。 对于经济和管理等复杂系统来讲,人类的经验知识起着至关重要的作用。语言动力学系统计算的基本单位是语言的基本单位“词”。因为词具有不确定性,本文利用区间二型模糊集合作为词的基本模型。根据是否建立了数学模型语言动力学系统分为I型语言动力学系统和II型语言动力学系统。本文的主要研究内容如下 研究了基于区间二型模糊集合的词计算的基本方法。根据是否建立数学模型,将词计算分为I型词计算和II型词计算。对于I型词计算,根据区间二型模糊集合的特点,重点研究了离散、半离散和连续区间二型模糊集合的词计算的基本方法。对于离散和半离散的区间二型模糊集合 采用区间二型模糊扩展原理对它们进行计算。对于连续区间二型模糊集合采用模糊分解原理对它们进行计算。对于II型词计算,利用Mamdani区间二型模糊推理方法进行计算。 介绍一阶线性I型语言动力学系统的数值解法,能控性和能观性条件和稳定性。然后推广到n阶线性语言动力学系统的数值解法,能控性和能观性条件和稳定性。针对系统矩阵、控制矩阵和输出矩阵均为正矩阵时的一类n阶线性语言动力学系统,给出它们的数值解法、能控性和能观性条件和稳定性。 研究了II型语言动力学系统的计算方法。对于II型语言动力学系统着重研究它的计算方法。对于自治II型语言动力学系统研究了它的不变语言向量。为了使语言向量达到设定的目标语言向量,设计了语言控制器。 初步探讨了区间二型模糊方法和胞空间方法的关系。介绍了模糊细胞和半离散区间二型模糊集合的对应关系。I型词计算和II型词计算和胞映射的对应关系以及I型语言动力学系统和II型语言动力学系统和胞空间搜索方法的关系。
Other AbstractTraditional conventional dynamic systems (CDS) have great effect on in the study of the physical systems and engineering systems, promoting the development of the modern science and technology and improving people's lives. However, with the people's research field extending from the engineering systems to the social systems, The limitations of conventional dynamic systems are exposed. The conventional dynamic systems based on accurate mathematical model are not feasible to study complex systems. For effective solutions to complex systems analysis, prediction and synthesis problem, this paper presents the linguistic dynamic system based on computing with words to analyze and solve complex systems. For complex systems, the human experience and knowledge play a vital role in dealing with the complex social systems. The basic unit of calculation in linguistic dynamic systems no longer is the number or symbol as the conventional dynamic systems, which is word as the basic units. Since the words are uncertainty, the element model of the words is interval type-2 fuzzy set. Whether a mathematical model is or not, the linguistic dynamic system is divided into type-I linguistic dynamic system and type-II linguistic dynamic system. The main research contents are as follows. The basic calculation method is researched about computing with words with the interval type-2 fuzzy sets. According to wether or not setting up the mathematical model, the computing with words is divided into type-I computing with words and type-II computing with words. To type-I computing with words, According to the characteristics of interval type-2 fuzzy sets, the basic methods of computing with words on discrete, semi-discrete and continuous interval type-2 fuzzy sets are focused on research. For the discrete and semi-discrete interval type-2 fuzzy sets, the interval type-2 fuzzy extension principle is used to compute with words. For the continuous interval type-2 fuzzy set, the fuzzy decomposition principle is used to proceed computing with words. To type-II computing with words, the Mamdani interval type-2 fuzzy inference method is used to proceed the image words from the original image words. The numerical procedure of the first-order linear linguistic dynamical systems is introduced, controllability and observability conditions and stability are researched. Then they are extended to those of the n-order linear linguistic dynamical systems. When the system matrix, control matrix an...
Other Identifier200518014628019
Document Type学位论文
Recommended Citation
GB/T 7714
赵亮. 基于区间二型模糊方法的词计算和语言动力学系统研究[D]. 中国科学院自动化研究所. 中国科学院研究生院,2009.
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