模糊推理三I算法的逻辑基础

在模糊推理理论中，近期问世的三I推理方法以逻辑蕴涵运算取代传统的合成运算，从根本上改进了传统的合成推理规则(即CRI方法)。本文基于模糊命题逻辑的形式演绎系统L^*和模糊谓词逻辑的一阶系统K^*，构建了一个完备的多型变元一阶系统Kms^*，并且将三I算法完全纳入了模糊逻辑的框架之中，从而为模糊推理奠定了严格的逻辑基础。     

模糊CRI算法及模糊推理的有效性研究

通过揭示模糊推理的一种CRI算法的逻辑原理,提出了模糊推理的一种新算法.并对单规则的CRI算法(或三Ⅰ算法)的重心(或最大隶属度)去模糊法的有效性进行了研究.发现在单规则的CRI算法(或三Ⅰ算法)的模糊推理中,当大前提的后件取对称模糊集时,采用重心去模糊法使得推理结果无效,而采用最大隶属度去模糊法可使得推理结果有效.     

基于Mamdani型模糊推理的震中烈度预测模型

对应用模糊推理进行系统预测进行了深入的研究,建立了以震级和震源深度为输入的基于Mamdani型模糊推理的震中烈度预测模型.并以四川地区震例数据为例,对数据信息提取,模糊规则建立等关键环节进行了详细的介绍,预测结果分析表明推理模型是可行和有效的.     

Gentzen型模糊推理

本文建立了能同时处理证据、规则的不确定性以及证据与规则近似匹配的Gentzen型模糊推理的语形方法．     

翼伞航迹跟踪多输入模糊控制

本文研究了翼伞系统的自主归航控制技术。采用输入信息少的模糊控制器会影响翼伞的控制精度,而当输入信息较多是会使模糊控制器的模糊规则判断复杂化,影响控制器的反应速度。本文基于因素空间理论,对多输入的翼伞航迹跟踪模糊控制器的模糊推理规则判断进行了简化处理。经简化后的模糊推理机制,在不损失输入信息和不损害模糊控制器的前提下,利用最少的输入信息达到相同的模糊推理结果,大大减小了不必要的模糊推理,降低了模糊控制器的计算负担,大大提高了翼伞航迹跟踪的实时控制效果。仿真结果证明了新方法的有效性。     

模糊控制系统的建模

提出一种基于模糊推理的关于控制系统的建模方法,称之为模糊推理建模法, 它可以作为不同于熟知的机理建模法和系统辨识建模法的第3种建模方法. 该方法根据模糊逻辑系统的插值机理将关于被控对象的模糊推理规则库转换为一类变系数非线性微分方程(组), 从而得到控制系统的数学模型;这样便解决了在模糊控制系统中被控对象难于建模的问题.     

加权抽取模糊推理中的评判方法

在真值流推理和加权模糊推理过程中,必然要遇到评判揄结论是否被证实的问题,本文针对多角度反映规则结论的情况提出了一种实用评判算法。     

基于合成规则的相似性推理及其在焊接参数设计中的应用

焊接过程是典型的复杂过程,应用模糊逻辑建立焊接参数推理系统可快速实现焊接工艺参数设计.近似推理机制是模糊系统研究和开发中的一个重要组成部分,在现有的相似性推理方法的基础上,融合经典的合成规则推理技术,提出一种新的基于合成规则的相似性推理方法.以CO_2保护焊焊接规范参数设计为背景介绍模糊推理在焊接领域的应用,运行结果表明,采用方法建立的模糊推理模型具有较高的推算精度,能够满足焊接工艺参数设计的要求.     

区间值模糊推理的三Ⅰ算法

模糊推理在控制和人工智能等领域已得到了广泛的应用，但其理论基础还不完善，王国俊教授提出的模糊命题逻辑的形式演绎系统和三Ⅰ算法为模糊推理奠定了严格的逻辑基础，本文把三Ⅰ算法用于区间值模糊推理，并且指出一般模糊推理是在区间退化为点时的特殊区间值模糊推理，从而把一般模糊推理纳入于区间值模糊推理的框架之内。     

基于模糊逻辑推理的改进多响应参数优化方法研究

研究一种基于模糊逻辑推理的改进多响应参数优化方法.通过满意度函数求解各个响应的满意度值,然后经过模糊逻辑推理将多个响应的满意度值转化为模糊推理等级(FRG).模糊推理规则可以充分考虑实际工艺操作经验和专家知识,利用响应间相互关系的机理和统计信息,得到的模糊推理等级能够客观反映多个质量特性的整体水平.将基于模糊逻辑推理的改进多响应参数优化方法运用到铣切削生产过程的参数优化设计中,使两个响应的粗糙程度均有所下降,验证了方法的有效性.     

An exponential separation between the parity principle and the pigeonhole principle

The combinatorial parity principle states that there is no perfect matching on an odd number of vertices. This principle generalizes the pigeonhole principle, which states that for a fixed bipartition of the vertices, there is no perfect matching between them. Therefore, it follows from recent lower bounds for the pigeonhole principle that the parity principle requires exponential-size bounded-depth Frege proofs. Ajtai (1990) previously showed that the parity principle does not have polynomial-size bounded-depth Frege proofs even with the pigeonhole principle as an axiom schema. His proof utilizes nonstandard model theory and is nonconstructive. We improve Ajtai's lower bound from barely superpolynomial to exponential and eliminate the nonstandard model theory.

Our lower bound is also related to the inherent complexity of particular search classes (see Papadimitriou, 1991). In particular, oracle separations between the complexity classes PPA and PPAD, and between PPA and PPP also follow from our techniques (Beame et al., 1995).     

基于粒子群算法的匹配小波的构建

本文研究了在波形匹配原则下的匹配小波的构建问题.利用结合结构化小波滤波器组理论和粒子群算法,获得了构造最优匹配小波的粒子群算法,推广了匹配小波的构建方法.     

一类拟线性奇摄动边值问题的激波性态(英文)

The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle.     

一类四阶非线性奇摄动方程的边值问题

利用匹配渐近展开法,讨论了一类四阶非线性方程的具有两个边界层的奇摄动边值问题．引进伸长变量,根据边界条件与匹配原则,在一定的可解性条件下,给出了外部解和左右边界层附近的内层解,得到了该问题的二阶渐近解,并举例说明了这类非线性问题渐近解的存在性．     

Large Deviation Theorems for Gaussian Processes and Their Applications in Information Theory

We discuss on the large deviation theorems for stationary Gaussian processes and their applications in information theory. The topics investigated here include error probability of string matching, error probabilities for random codings, and a conditional limit theorem which justifies the maximum entropy principle.     

Harmonic Algebraic Curves and Noncrossing Partitions

Motivated by Gauss's first proof of the Fundamental Theorem of Algebra, we study the topology of harmonic algebraic curves. By the maximum principle, a harmonic curve has no bounded components; its topology is determined by the combinatorial data of a noncrossing matching. Similarly, every complex polynomial gives rise to a related combinatorial object that we call a basketball, consisting of a pair of noncrossing matchings satisfying one additional constraint. We prove that every noncrossing matching arises from some harmonic curve, and deduce from this that every basketball arises from some polynomial.     

One-Bit Compressed Sensing by Greedy Algorithms

Sign truncated matching pursuit (STrMP) algorithm is presented in this paper. STrMP is a new greedy algorithm for the recovery of sparse signals from the sign measurement, which combines the principle of consistent reconstruction with orthogonal matching pursuit (OMP). The main part of STrMP is as concise as OMP and hence STrMP is simple to implement. In contrast to previous greedy algorithms for one-bit compressed sensing, STrMP only need to solve a convex and unconstrained subproblem at each iteration. Numerical experiments show that STrMP is fast and accurate for one-bit compressed sensing compared with other algorithms.     

典型案例系统中的模式识别问题—模型与算法

建立典型案例系统中的模式识别问题的数学模型，并根据特征取值的不同对其分类，进而讨论不同类型伯特征的取值之间贴近度的定义方法，以及模式空间的匹配算子的选取原则，最后通过设定阈值来定义输出模式集。     

Model recovery for Hammerstein systems using the auxiliary model based orthogonal matching pursuit method

This article investigates parameter and order identification of a block-oriented Hammerstein system by using the orthogonal matching pursuit method in the compressive sensing theory which deals with how to recover a sparse signal in a known basis with a linear measurement model and a small set of linear measurements. The idea is to parameterize the Hammerstein system into the linear measurement model containing a measurement matrix with some unknown variables and a sparse parameter vector by using the key variable separation principle, then an auxiliary model based orthogonal matching pursuit algorithm is presented to recover the sparse vector.The standard orthogonal matching pursuit algorithm with a known measurement matrix is a popular recovery strategy by picking the supporting basis and the corresponding non-zero element of a sparse signal in a greedy fashion. In contrast to this, the auxiliary model based orthogonal matching pursuit algorithm has unknown variables in the measurement matrix. For a K-sparse signal, the standard orthogonal matching pursuit algorithm takes a fixed number of K stages to pick K columns (atoms) in the measurement matrix, while the auxiliary model based orthogonal matching pursuit algorithm takes steps larger than K to pick K atoms in the measurement matrix with the process of picking and deleting atoms, due to the gradually accurate estimates of the unknown variables step by step.The auxiliary model based orthogonal matching pursuit algorithm can simultaneously identify parameters and orders of the Hammerstein system, and has a high efficient identification performance.     

非线性奇摄动两点边值问题的激波性态

在适当的条件下，利用奇摄动理论和匹配原理，讨论了一类非线性奇摄动两点边值问题的激波性态，构造了原问题的内部和外部解，较简捷地得到了与边界条件相对应的具有激波性态的解的表达式以及位于区间内部的激波位置。