模糊关系方程

<正> 模糊关系方程是模糊数学的一个基本课题,近年来,国内外在这方面开展了许多研究工作,但至今还有不少问题没有得到比较理想的结果.本文讨论了一般模糊关系方程的求解问题,对一类最常见的模糊关系方程从理论上弄清了它的解集结构并给出了一种实际解法,从而使问题得到比较彻底的解决.     

不完备直觉模糊信息系统的属性约简

利用优势关系,可对完备直觉模糊信息系统与决策信息表进行属性约简.将优势关系改进为广义优势关系,在此基础上构建了不完备直觉模糊信息系统与决策信息表的辨识矩阵,得到了求解属性约简与相对约简的具体方法.     

求解具有max-t-norm合成算子的模糊关系不等式

研究一类具有max-t-norm合成算子的模糊关系不等式,该问题是模糊关系方程以及区间值模糊关系方程的推广.通过分析其解集的特点,提出一个基于筛选原则求解该类问题的算法,并给出数值算例说明该算法的有效性.     

模糊数值函数积分原函数的可导性问题

基于模糊分析学微分理论的推广和模糊微分方程求解的需要，对模糊数值函数积分原函数的可导性问题进行讨论，完备模糊数值函数微积分的理论体系。     

剩余格上inf-→与inf-■合成模糊关系方程的求解

本文在广义剩余格上研究inf-→与inf-■合成模糊关系方程的求解问题,首先分别给出inf-→与inf-■合成模糊关系方程有解的充分条件,由此分别给出inf-→与inf-■合成模糊关系方程的一个特解,进一步给出它们解集的子集,然后在一定条件下分别构造出inf-→与inf-■合成模糊关系方程的所有极大解,以及极大解的个数和表达形式,并给出解集。     

幂模糊数方程和二次模糊方程的结构元求解方法

定义了幂模糊数和幂模糊数方程,基于结构元方法研究了幂模糊数运算和幂模糊数方程的求解,给出了隶属函数的表达式.同时,利用区间[-1,1]上的单调函数将二次模糊方程的求解问题转化为经典参数方程组的求解问题,给出了二次模糊方程解存在的充要条件,并辅以数值例子.     

Lawson紧的代数L-domain递归方程的逻辑形式

本文的目的是为Lawson紧的代数L-domain递归方程及其解提供一种逻辑刻画。基于N-序列演算上的子系统关系,证明了N-序列演算之集是定向完备的,并在这一定向完备偏序集上引入了三种连续构造算子：提升,联结和以及分离和。从而求解domain结构递归方程的问题可归结为如何构建连续映射的不动点。     

完备Brouwer格上有限sup-inf合成Fuzzy关系方程解集的一些性质

主要对完备Brouwer格上sup-inf合成的Fuzzy关系方程的解作了深入的讨论.首先讨论了在完备Brouwer格中方程解的情况,并在有解时给出了求解所有极小解的方法.进一步,刻画了sup-inf合成Fuzzy关系方程解集的结构.     

微分方程模糊初值问题的解

研究了一阶线性微分方程模糊初值问题,利用模糊微分方程的刻画方程和初值之间的关系,给出了一阶线性微分方程模糊初值问题的一种求解方法,讨论了同基于Hukuhara微分求解方法之间的关系,证明了在一定条件下两种方法是等价的,文中的实例说明了这一点.     

模糊关系方程在预测深部开采地面下沉中的应用

根据深部矿体开采岩体移动变形的特点,建立了地面下沉值与影响因素间的模糊关系方程.确定出各指标间的模糊关系并对模糊关系方程进行了求解;然后通过模糊变换得出采区下沉的预测值.通过工程实例对比分析结果表明,理论分析结果与实测资料是一致的.     

Fuzzy perturbation analysis,part I: Directional perturbation

In this paper, a new idea, fuzzy perturbation, is advanced. The stability of the solutions of a fuzzy relation equation and the generalized solution of the unsolvable equation are defined by means of this idea. Thereupon, a part of the theory of fuzzy perturbation analysis, fuzzy directional perturbation, is formed. By use of the theory an approach to solving two open problems in the inverse problem of fuzzy multifactorial decision is made.     

完全分配格上的伪补及其应用

定义完全分配格上的伪补 ,讨论伪补的性质 ,给出模糊矩阵有广义逆及模糊关系方程有解的充分必要条件。     

极小解法求解最大-最小型关系方程的系统研究

最大-最小型关系方程已有许多学者进行过研究并给出一些解法,这些解法在应用中仍显得过于复杂.本文在文献[1]的基础上对最大-最小型关系方程的极小解的性质和特点进行了系统的研究,并对文献[1]提出的求解这类方程的图法和分枝法在理论上进行了补充和完善.研究表明,图法和分枝法是求解最大-最小型关系方程的有效方法.     

模糊线性回归模型的约束最小二乘估计

自Tanaka等1982年提出模糊回归概念以来,该问题已得到广泛的研究。作为主要估计方法之一的模糊最小二乘估计以其与统计最小二乘估计的密切联系更受到人们的重视。本文依据适当定义的两个模糊数之间的距离,提出了模糊线性回归模型的一个约束最小二乘估计方法,该方法不仅能使估计的模糊参数的宽度具有非负性而且估计的模糊参数的中心线与传统的最小二乘估计相一致。最后,通过数值例子说明了所提方法的具体应用。     

Reachable solution set of a fuzzy relation equation

The largest element of the solution set of a fuzzy relation equation has been found by E. Sanchez (Inform. and Control30 (1976), 38–48) but the smallest element does not exist. It is difficult to expose the solution of the fuzzy relation equation. In the case of the determinate relation equations, complete consequences have been found by Wang Peizhuang and Yuan Meng (“Relation Equation and Relation Inequalities,” Selected papers on fuzzy subsets, Beijing Normal University, March 1980). In the case of the fuzzy relation equations, Wang and Yuan have given a class of special solutions which probably possesses some minimality characterizations. In this paper, the reachable solution set of the fuzzy relation equation is given. For the fuzzy relation equation on the finite sets, a neat and efficient method for solving it is given.     

可加性模糊系统(AFS)权系数W的最小二乘估计

本文对模糊规则的前件进行非模糊化,从而给出了被广泛应用于现代控制理论中的可加性模糊系统（ＡＦＳ）权系数Ｗ 的最小二乘估计。     

Stability analysis of fuzzy linear differential equations

Differential equation is a very important field of study not only in theory but in applications, and stochastic differential equation is also a significant branch of research in theory and applications. Based on the concepts of fuzzy process and fuzzy differential equation, we present some concepts of stability for fuzzy differential equations. Furthermore we propose the sufficient and necessary conditions of stability for fuzzy linear differential equations.     

Fuzzy modelling with tolerances

We consider the problem of the resolution of fuzzy equation systems: A certain number of fuzzy inputs and outputs is given. How can we determine a fuzzy relation which describes the behaviour of the object under consideration? When attributing this problem to fuzzy equations in the classical sense it may happen that a solution does not exist. Therefore we introduce fuzzy tolerances as an extension of the solvability conception. For this problem we get the whole solution set by means of posets. Moreover, we consider the inverse problem: How to determine tolerances to get consistency (i.e. at least one solution) for the arising equation system.     

Wave splitting of the Timoshenko beam equation in the time domain

In recent years, wave splitting in conjunction with invariant imbedding and Green's function techniques has been applied with great success to a number of interesting inverse and direct scattering problems. The aim of the present paper is to derive a wave splitting for the Timoshenko equation, a fourth order PDE of importance in beam theory. An analysis of the hyperbolicity of the Timoshenko equation and its, in a sense, less physical relatives-the Euler-Bernoulli and the Rayleigh equations-is also provided.     

模糊矩阵方程解的结构

讨论模糊矩阵方程ＡＸ＝ Ｃ的解的结构,当Ｃ为模糊常矩阵时,给出了方程的最大解和极小解的求法,讨论了方程存在最小解的充分必要条件