修正的模糊最小一乘线性回归

对文献[1]提出的基于对称三角模糊数的模糊最小一乘线性回归进行修正和扩展,给出模糊最小一乘线性回归模型的三种不同形式,并将其转化为线性规划或非线性规划问题进行求解。最后,给出几个数值实例,通过计算和比较,结果表明三种模糊最小一乘线性回归模型都具有非常好的拟合性。     

基于EEMD与模糊回归的投资组合选择模型及实证

随着模糊理论的不断发展与其在证券市场的广泛应用,越来越多的学者关注到参数模糊化对投资组合优化具有重要作用。本文利用集合经验模态分解(EEMD)和模糊线性回归相结合的预测方法,构建了基于对称三角模糊数的投资组合模型。并将提出的模型与集合经验模态分解和普通最小二乘结合的方法、单一模糊线性回归方法进行了对比分析,结果表明基于集合经验模态分解和模糊线性回归建立的投资组合模型最优,这对构建最优投资组合具有参考意义。     

拟合模糊观测数据的线性回归模型

本文讨论了实验观测数据为一般模糊数的线性最优拟合问题，通过定义模糊数空间中的距离，建立了模糊数空间到模糊数空间的回归模型，证明了最小二乘问题的解与其正则方程组的解的一致性，进而由正则方程组导出了问题的显式解。本模型的计算简便，具有实用价值。     

基于结构元最小二乘序的模糊线性回归

在具有模糊观测数据的线性回归问题中,通过定义模糊序指标实现模糊数的排序,借助经典最小二乘法原理,给出了使平方误差和在此排序方法下达到最小的模糊回归系数最小二乘序估计方法。三个例子的结果表明,文中的最小二乘方法能很好的对输入和输出为模糊数,回归系数为精确值的回归模型进行估计,更重要的是,此方法不仅对三角模糊数适用,对其他类型的模糊观测数据也适用。     

数值输入模糊输出数据的最小二乘回归模型

本文给出了一个拟合数值输入模糊数输出数据的线性回归模型,证明了模型的解存在且唯一,并得到了解的表达式。     

带模糊回归参数的线性回归模型

本文讨论了数值输入模糊数输出的观测数据的线性最小二乘拟合问题，建立了数值空间到模糊数空间的带模糊回归参数的线性回归模型，证明了模型解的存在性和唯一性，并得到了解的表达式。本模型应用简便，具有实用价值。     

一个新的最优模糊存储模型

提出一个新的具有积压定单的关于模糊订购量的模糊存储模型.在模糊函数原理下,给出了模糊总存储成本.为了寻找最优解,把最优模糊存储模型转化为双目标最优化模型,利用L ingo8.0求解不等式约束问题,我们发现最优解都是确定的实数.此外,当模糊订购量和模糊总需求都是三角形(或权重均为1/2梯形)模糊数时,我们提出模型的最优解与经典的具有积压定单存储模型具有相同的结果.     

一类不分明时间序列的回归预测

研究了一类不分明时间序列的线性回归预测问题,通过模糊数空间中的距离,建立了模糊环境中最小二乘回归模型,证明了回归模型解的存在性和唯一性,并给出了确定模型的模糊参数及检验模型拟合度的计算公式。     

一类系数为梯形模糊数的两层线性规划

讨论了一类系数为梯形模糊数的两层线性规划问题,首先是利用模糊结构元理论将梯形模糊数去模糊化,将其转化成常规的两层线性问题,并验证其去模糊化后的常规的两层线性规划的最优解与系数为梯形模糊数的两层线性规划问题的最优解一致,并给出具体的算法,数例进行验证.     

求解一类模糊线性微分系统的结构元方法

基于模糊结构元方法,研究了由对称模糊结构元线性生成的一般模糊线性微分系统和双重的一般模糊线性微分系统,给出了模糊线性微分系统解存在的充要条件,得到了结构元线性生成的齐次、非齐次以及双重一般模糊线性微分系统求解方法。最后,给出了这类系统的实际应用。     

系数为LR-型模糊数的模糊线性最小二乘回归

针对输入、输出以及系数为LR-型模糊数的情况,建立模糊线性回归模型,提出该模型的最小二乘估计以及模型性能评价方法。当输入、输出以及系数都退化为精确值时,该估计退化为经典的最小二乘估计。该方法不仅适用于三角模糊数,也适用于其它LR-型模糊数(如指数型模糊数)。数值模拟表明,该方法的拟合效果较好。     

Linear fuzzy regression

This paper presents an approach which is useful for regression analysis in the case of heterogeneity of a set of observations, for which regression is evaluated. The proposed procedure consists of two stages. First, for a set of observations, fuzzy classification is determined. Due to this, homogenous classes of observations which are of hyperellipsoidal shape, are obtained. Then for each fuzzy class, the so called linear fuzzy regression is evaluated.

In the paper the method of calculating linear fuzzy regression coefficients is given. It is a generalized version of the least squares method. The formula for the values of coefficients is given. Some properties of linear fuzzy regression are analyzed. It is proved that in one- and two-dimensional cases, the formulae are analogous to those for usual regression. A measure of goodness-of-fit and the method of determination of the number of fuzzy classes are also given.

Presented examples indicate the superiority of fuzzy regression in comparison to usual regression in the case of heterogenous observations.     

基于多目标规划法的模糊线性回归分析

讨论输入、输出均为模糊数,回归系数为实数时的模糊线性回归分析。由于模糊最小二乘线性回归容易受异常值的影响,而最小一乘法能有效地降低回归模型的误差。为此,基于最小一乘法,建立多目标规划模型并将其转化为非线性规划问题进行求解,从而实现模糊线性回归模型的参数估计。最后,结合一个数值实例,验证和比较该方法的合理性和优越性。     

Evaluation of fuzzy regression models by fuzzy neural network

In this paper, a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy linear and nonlinear regression models with fuzzy output and crisp inputs, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.     

基于具有LR型模糊输出回归模型的保费预测

在保费预测研究中,提出了一种基于模糊回归模型的预测方法.采用模糊最小二乘法,针对清晰输入和LR型模糊输出,在考虑输出量隶属函数类型存在差异问题基础之上,得到模型回归系数的迭代解.通过最小二乘估计的定性分析,给出检验模型拟合度的指标.结合保费数据的预测结果表明模型可行且具有较强的解释能力.     

Inherited Fuzzy Interpolation Based on the Inherited Lower-upper Factorization

In this paper, a new scheme is proposed to find the fuzzy interpolation polynomial. In this case, the nodes are crisp data and the values are fuzzy numbers. In order to obtain the interpolation polynomial, a linear system is solved with crisp coefficients matrix and fuzzy right hand side. Then, the inherited lower-upper (LU) triangular factorization and inherited interpolation are applied to solve this system. The examples illustrate the applicability, simplicity and efficiency of the proposed method.     

Intuitionistic fuzzy linear regression analysis

Linear regression analysis in an intuitionistic fuzzy environment using intuitionistic fuzzy linear models with symmetric triangular intuitionistic fuzzy number (STriIFN) coefficients is introduced. The goal of this regression is to find the coefficients of a proposed model for all given input–output data sets. The coefficients of an intuitionistic fuzzy regression (IFR) model are found by solving a linear programming problem (LPP). The objective function of the LPP is to minimize the total fuzziness of the IFR model which is related to the width of IF coefficients. An illustrative example is also presented to depict the solution procedure of the IFR problem by using STriIFNs.     

Evaluation of fuzzy linear regression models by comparing membership functions

Fuzzy linear regression models can provide an estimated fuzzy number that has a fuzzy membership function. If a point that has the highest membership value from the estimated fuzzy number is not within the support of the observed fuzzy membership function, a decision-maker can have high risk from the estimate. In this study a modification of fuzzy linear regression analysis based on a criterion of minimizing the difference of the fuzzy membership values between the observed and estimated fuzzy numbers is proposed. Two numerical examples are used to evaluate the fuzzy regression models.