模糊维结构及模糊多维数据模型

基于模糊等价关系，提出一种支持非完全划分的模糊维结构模型，并对模糊维的层次聚集关系，数据立方体和OLAP分析操作进行了形式化描述，从而形成了一种较完整的模糊多维数据模型。     

基于模糊GJR-GARCH模型的波动率估计

基于模糊数学和模糊时间序列分析理论,在模糊GARCH与GJR-GARCH模型的基础上建立模糊GJR-GARCH模型,并用遗传算法估计了该模型的参数。实证发现沪深两市的收益波动率具有明显的非对称性,相对于普通的GARCH、GJR-GARCH和模糊GARCH模型,模糊GJR-GARCH模型能更好的处理收益率的波动群聚性、时变性和非对称性,具有更好的估计精度。     

模糊积分变换与模糊Choquet积分的一致连续性

在一般非负单调函数空间 m[0 ,a]上引入模糊积分变换与距离的概念 ,证明了这种模糊积分变换与模糊 Choquet积分在 m[0 ,a]上关于这种距离是一致连续的 ,从而说明当 m[0 ,a]上两个函数变化不大时 ,不会使相应的模糊积分变换与模糊 Choquet积分产生较大的变化 .     

直觉模糊变换半群的积与覆盖关系

提出了直觉模糊变换半群的(全)直积,圈积,直觉模糊变换半群的覆盖的定义,利用代数的手段讨论了直觉模糊变换半群的积的结合性质,研究了直觉模糊变换半群的积的覆盖关系.     

估计运动模糊图像方向角的数学模型研究

从实拍的运动模糊图像出发,建立了数学模型来估计运动模糊的方向角.经理论推导,得出了运动模糊方向角、图像尺寸和频谱图像中平行条纹方向角三者的关系,将问题转化为估计频谱平行条纹方向角.在模型求解部分,分析了常用的Radon变换法以及两种改进方法即Gabor变换法和频谱分块法的不足,并提出了基于频谱边缘检测的改进方法.数值实验部分比较了三种方法,结果表明,方法的估计精度更高,具有更广泛的应用性.     

基于模糊数变换的DEA模型与应用

在数据包络分析(DEA)的C^2R模型的基础上，建立FC^2R模型。但现有的FC^2R模型，要求模糊输入输出指标值之间满足一定的严格条件，这在实际应用中有一定的局限性。为此本文在FC^2R模型的基础上，提出了一种基于模糊数变换的DEA模型(α-FC^2R模型)，拓展了传统DEA的应用范围，并将其应用于综合评价，取得了很好效果。     

具有投资限制的风险资产模糊随机投资组合模型

研究了模糊随机环境下风险资产投资组合选择问题.利用模糊随机变量刻画风险资产的收益率,建立了具有投资限制的风险资产投资组合选择的一般模糊随机均值-方差模型,该模型包括了是否允许卖空及具有投资比例下界约束的情况.在此基础上,提出了具有梯形模糊随机收益率的具体投资组合优化模型,这些模型能够转化为二次规划问题求解.最后,利用上证50指数中的9种股票对模型进行了实证分析,结果表明模型能够有效分散非系统性风险.     

基于语言变量模糊评价的可信软件非功能需求权衡模型

提出了一个模糊定性定量的软目标相互依存图FQQSIG模型(Fuzzy Qualitative and Quantitative Softgoal Interdependency Graphs)来分析可信软件(Trustworthy Software,TS)中的非功能需求(Non-Functional Requirements,NFRs)的相关性.首先描述了一个NFRs层次分解图,专家团队并对NFRs的重要性程度进行语言变量形式的模糊定性评价,然后再用梯形模糊数和RAGE(RAndom GEneration)随机仿真算法来完成定性到定量数据的转化,最后再提出关系矩阵算法实现NFRs节点贡献值的计算以及应用FQQSIG模型进行NFRs节点权衡.     

一种基于CS-FCM算法的模糊时间序列预测模型

为了发挥模糊理论在不确定性预测中的优势并保留模糊时间序列(FTS)预测模型的可解释性,本文针对目前应用广泛的模糊C均值聚类(FCM)算法进行改进,提出了一种基于布谷鸟搜索的FCM (CS-FCM)算法.将CS-FCM算法用于模糊时间序列模型的非均匀论域划分与数据的模糊化处理,建立一种基于CS-FCM算法的模糊时间序列预测模型.该算法可实现聚类中心的全局寻优,降低传统FCM算法易陷入局部极小值带来的误差,提高模型预测精度.实证分析结果表明, CS-FCM算法的适应度优于FCM算法,本文模型的预测误差小于经典模糊时间序列预测模型,验证了新预测模型的有效性.     

模糊数限定运算、广义限定运算与广义运算

在综合分析模糊数的限定运算和广义限定运算的基础上,通过扩展模糊数结构元的表示方法,将模糊数结构元理论中的变换函数的单调性推广到连续性(至多在x=0处有一个间断点),提出了模糊数的广义运算,试图解决模糊数运算出现的多种问题。     

A note on chance constrained programming with fuzzy coefficients

This paper deals with nonlinear chance constrained programming as well as multiobjective case and goal programming with fuzzy coefficients occurring in not only constraints but also objectives. We also present a fuzzy simulation technique for handling fuzzy objective constraints and fuzzy goal constraints. Finally, a fuzzy simulation based genetic algorithm is employed to solve a numerical example.     

模糊数的相等、同一与等式限定运算

讨论了在模糊数运算中相等与同一的区别,在Klir的模糊数限定运算基础上提出了模糊数的等式限定运算以及等式限定运算的结构元表示方法,解决了传统模糊数运算的不可逆问题.通过模糊数的结构元表示方法,将其等式限定运算转换为两个同序单调函数的运算,这不仅仅给出等式限定运算的可操作形式,同时对于求解模糊数方程也给出了具体的计算方法.     

Systems of linear fuzzy constraints

Linear Fuzzy constraints are linear constraints where coefficients are fuzzy numbers. This paper demonstrates that two points of view can be considered to extend classical linear constraints: either tolerance constraints, or approximate (in)equality constraints can be obtained. Resolution of systems of linear fuzzy constraints is shown to be made easier by the use of fuzzy numbers analytically represented through a given type of membership function and three parameters. Solution methods are provided in the case of non fuzzy variables; as an illustration, some numerical examples are presented. The fuzzy variable case is also evoked.This paper is part of Purdue University Electrical Engineering technical report TR-EE 78-13.     

A new methodology for crisp equivalent of fuzzy chance constrained programming problem

This paper deals with a chance constrained programming model, where both fuzziness and randomness are present in the objective function and constraints. The concept of fuzzy random variable, mean and variance of fuzzy random variable, minimum of fuzzy numbers are used in the model. The methodology is verified through a numerical example.     

A dual approach to solve the fuzzy linear programming problem

A concept of fuzzy objective based on the Fuzzification Principle is presented. In accordance with this concept, the Fuzzy Linear Mathematical Programming problem is easily solved. A relationship of duality among fuzzy constraints and fuzzy objectives is given. The dual problem of a Fuzzy Linear Programming problem is also defined.     

模糊数和模糊值函数的等式限定运算

通过模糊数的结构元表示方法,利用两个单调函数的自反单调变换构造了等式限定算子,推广了文[6]中的等式限定运算,处理了存在负模糊情况下关于乘法运算的不可逆问题.同时,本文还将等式限定运算推广到模糊值函数上,提出了模糊值函数等式限定运算的结构元方法,解决了模糊值函数运算的不可逆问题.     

Linear programming with fuzzy parameters: An interactive method resolution

This paper proposes a method for solving linear programming problems where all the coefficients are, in general, fuzzy numbers. We use a fuzzy ranking method to rank the fuzzy objective values and to deal with the inequality relation on constraints. It allows us to work with the concept of feasibility degree. The bigger the feasibility degree is, the worst the objective value will be. We offer the decision-maker (DM) the optimal solution for several different degrees of feasibility. With this information the DM is able to establish a fuzzy goal. We build a fuzzy subset in the decision space whose membership function represents the balance between feasibility degree of constraints and satisfaction degree of the goal. A reasonable solution is the one that has the biggest membership degree to this fuzzy subset. Finally, to illustrate our method, we solve a numerical example.     

On fuzzy random multiobjective quadratic programming

In this paper, a multiobjective quadratic programming problem having fuzzy random coefficients matrix in the objective and constraints and the decision vector are fuzzy pseudorandom variables is considered. First, we show that the efficient solutions of fuzzy quadratic multiobjective programming problems are resolved into series-optimal-solutions of relative scalar fuzzy quadratic programming. Some theorems are proved to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients, having decision vectors as fuzzy variables. At the end, numerical examples are illustrated in the support of the obtained results.     

Fuzzy modelling environment for designing fuzzy controllers

Fuzzy control algorithms are developed based on fuzzy models of systems. The control issues are posed as multiobjective optimization problems involving goals and constraints imposed on system's variables. Two basic design modes embrace on- and off-line modes of control development. The first type of design deals with the time and state-dependent objectives and pertains to control determination based upon the current state of the fuzzy model. The second design mode gives rise to an explicit form of a fuzzy controller that is learned based on a given list of state-control associations. Both the fuzzy models as well as fuzzy controllers are realized as logic processors.     

基于模糊需求的多产品供应商选择的多目标规划模型

由决策于环境的不确定性,供应商选择问题存在大量的模糊信息,传统的确定性规划模型已经不能够很好地处理此类问题。本文基于模糊需求量信息,对于多产品供应商问题建立了模糊多目标规划模型。同时考虑到各目标及约束的重要性程度不同的影响,通过引进适当的权重对多目标规划模型进行求解。文中结合实际算例验证模型的可行性和有效性。