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。     

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。     

纵向数据半参数回归模型的估计方法

本文考虑纵向数据半参数回归模型,通过考虑纵向数据的协方差结构,基于Profile最小二乘法和局部线性拟合的方法建立了模型中参数分量、回归函数和误差方差的估计量,来提高估计的有效性,在适当条件下给出了这些估计量的相合性.并通过模拟研究将该方法与最小二乘局部线性拟合估计方法进行了比较,表明了Profile最小二乘局部线性拟合方法在有限样本情况下具有良好的性质.     

基于广义最大熵的具有模糊输入输出的回归模型的参数估计

模糊回归是在模糊系统中建立因变量与一组自变量之间关系的重要工具,以评估模糊自变量如何影响模糊响应变量的过程。当系统中出现小样本或者非列满秩设计矩阵时,模糊最小二乘法可能得出偏误估计。本文基于文献[13]中的多元线性回归模型,利用广义最大熵方法,针对模糊输入模糊输出数据,给出线性回归模型的参数估计和算法步骤。当输入或输出数据退化为清晰值时,该估计退化为清晰输入模糊输出或者模糊输入清晰输出的回归模型参数估计。本文结合模拟数据和实例数据,将广义最大熵方法与模糊最小二乘方法、岭估计方法进行比较研究,结果显示广义最大熵方法的可行性和有效性。     

PP回归方法在预测模型中的应用－用PP回归建立“积累”“消费”模型

本文利用ＰＰ回归方法,建立“积累”“消费”回归模型,并与最小二乘法拟合的线性回归模型相比较,说明用ＰＰ回归建立的模型预测精度较高．     

PP回归方法在预测模型中的应用－用PP回归建立“积累”“消费”模型

本文利用ＰＰ回归方法,建立“积累”“消费”回归模型,并与最小二乘法拟合的线性回归模型相比较,说明用ＰＰ回归建立的模型预测精度较高．     

金融区间序列分析及其预测的初步评价

金融市场中的实际观测数据,除随机性外往往还带有模糊性,这样的观测数据通常以观测区间的形式给出,例如,当我们谈及某日的上证指数时,其观测值总是在最低点与最高点之间波动。观测值的这种不确定性来自于多重隶属现象,而非随机现象,我们称这种不确定性为模糊性。不确定性问题通常含有两种意义上的分类:一类是随机不确定性,人们依靠概率统计方法进行处理;另一类是非随机性的不确定性,即为模糊性问题,通常利用模糊集合理论来进行研究。本文将在模糊数学理论基础上,利用回归分析方法,构建模糊金融时间序列模型,并利用FLP(模糊线性规划)方法来估计模型的未知参数。为了合理评价拟合效果,我们将根据测量模糊集合间的择近原则,给出利用样本平均贴近度来评价模型拟合效果的一个准则。实证研究将讨论金融模糊时间观测序列的建模、参数估计,并对模型的实际拟合效果和预测效果做初步评价。     

模糊数据的线性回归模型

研究观测数据为模糊数据的统计线性回归模型 ,由该模型所得回归系数非模糊 ,易于应用。对于对称三角模糊数据一元线性回归给出最优解的解析表达式 ;将对称三角模糊数多元线性回归问题给出转化为一类二次规划问题的方法 ;证明了最优解的存在性和估计量的无偏性。     

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。     

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。     

Prediction of retinopathy in diabetic patients using type-2 fuzzy regression model

Due to the small sample size of data available in medical research and the levels of uncertainty and ambiguity associated with medical data, some researchers have employed fuzzy regression models to find the relationship between outcomes and explanatory variables in medical decision-making. The advantages of regression models are their ability to handle small sample sizes while fuzzy logic can model vagueness, thus making fuzzy regression a popular model among researchers. In addition, the high levels of uncertainty in medical data encourage the use of type-2 fuzzy which is capable of handling such uncertainty. The current paper proposes an interval type-2 fuzzy regression model for predicting retinopathy in diabetic patients. The results of the present work shall prevent unnecessary testing of diabetic patient. This study also aims to assist patients and the healthcare community to reduce the cost of diabetes control and treatment by optimizing the number of check-ups.     

Parametric regression analysis of imprecise and uncertain data in the fuzzy belief function framework

In this paper, parametric regression analyses including both linear and nonlinear regressions are investigated in the case of imprecise and uncertain data, represented by a fuzzy belief function. The parameters in both the linear and nonlinear regression models are estimated using the fuzzy evidential EM algorithm, a straightforward fuzzy version of the evidential EM algorithm. The nonlinear regression model is derived by introducing a kernel function into the proposed linear regression model. An unreliable sensor experiment is designed to evaluate the performance of the proposed linear and nonlinear parametric regression methods, called parametric evidential regression (PEVREG) models. The experimental results demonstrate the high prediction accuracy of the PEVREG models in regressions with crisp inputs and a fuzzy belief function as output.     

Upper and lower approximation models in interval regression using regression quantile techniques

In this paper, we propose new interval regression analysis based on the regression quantile techniques. To analyze a phenomenon in a fuzzy environment, we propose two interval approximation models. Without using all data, we first identify the main trend from the designated proportion of the given data. To select the main part of data to be analyzed, we introduce the regression quantile techniques. The obtained model is not influenced by extreme points since it is formulated from the center-located main proportion of the given data. After that, the interval regression model including all data can be identified based on the acquired main trend. The obtained interval regression model by the main proportion of the given data is called the lower approximation model, while interval regression model by all data is called the upper approximation model for the given phenomenon. Also it is shown that, from the lower approximation model (main trend) and the upper approximation model, we can construct a trapezoidal fuzzy model. The membership function of this fuzzy model is useful to obtain the locational information for each observation. The characteristic of our approach can be described as obtaining the upper and lower approximation models and combining them to be a fuzzy model for representing the given phenomenon in a fuzzy environment.     

Intelligent data analysis and model interpretation with spectral analysis fuzzy symbolic modeling

This paper proposes fuzzy symbolic modeling as a framework for intelligent data analysis and model interpretation in classification and regression problems. The fuzzy symbolic modeling approach is based on the eigenstructure analysis of the data similarity matrix to define the number of fuzzy rules in the model. Each fuzzy rule is associated with a symbol and is defined by a Gaussian membership function. The prototypes for the rules are computed by a clustering algorithm, and the model output parameters are computed as the solutions of a bounded quadratic optimization problem. In classification problems, the rules’ parameters are interpreted as the rules’ confidence. In regression problems, the rules’ parameters are used to derive rules’ confidences for classes that represent ranges of output variable values. The resulting model is evaluated based on a set of benchmark datasets for classification and regression problems. Nonparametric statistical tests were performed on the benchmark results, showing that the proposed approach produces compact fuzzy models with accuracy comparable to models produced by the standard modeling approaches. The resulting model is also exploited from the interpretability point of view, showing how the rule weights provide additional information to help in data and model understanding, such that it can be used as a decision support tool for the prediction of new data.     

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.     

Detecting fuzzy relationships in regression models: The case of insurer solvency surveillance in Germany

We develop a test for the fuzziness of regression coefficients based on the Tanaka et al. (1982) and He et al. (2007) possibilistic fuzzy regression models. We interpret the spread of the regression coefficients as a statistic measuring the fuzziness of the relationship between the corresponding independent variable and the dependent variable. We derive test distributions based on the null hypothesis that such spreads could have been obtained by estimating a possibilistic regression with data generated by a classical regression model with random errors. As an example, we show how our test detects a fuzzy regression coefficient in a solvency prediction model for German property-liability insurance companies.     

Quadratic interval innovation diffusion models for new product sales forecasting

An appropriate sales forecasting method is vital to the success of a business firm. The logistic model and the Gompertz model are usually adopted to forecast the growth trends and the potential market volume of innovative products. All of these models rely on statistics to explain the relationships between dependent and independent variables, and use crisp parameters. However, fuzzy relationships are more appropriate for describing the relationships between dependent and independent variables; these relationships require less data than traditional models to generate reasonable estimates of parameters. Therefore, we have combined fuzzy regression with the logistic and Gompertz models to develop a quadratic-interval Gompertz model and a quadratic-interval logistic model, and we applied the models to three cases. Our practical application of the two models shows that they are appropriate tools that can reveal the best and worst possible sales volume outcomes.     

Fuzzy interaction regression for short term load forecasting

Electric load forecasting is a fundamental business process and well-established analytical problem in the utility industry. Due to various characteristics of electricity demand series and the business needs, electric load forecasting is a classical textbook example and popular application field in the forecasting community. During the past 30 plus years, many statistical and artificial intelligence techniques have been applied to short term load forecasting (STLF) with varying degrees of success. Although fuzzy regression has been tried for STLF for about a decade, most research work is still focused at the theoretical level, leaving little value for practical applications. A primary reason is that inadequate attention has been paid to the improvement of the underlying linear model. This application-oriented paper proposes a fuzzy interaction regression approach to STLF. Through comparisons to three models (two fuzzy regression models and one multiple linear regression model) without interaction effects, the proposed approach shows superior performance over its counterparts. This paper also offers critical comments to a notable but questionable paper in this field. Finally, tips for practicing forecasting using fuzzy regression are discussed.     

A rule-based development of incremental models

In the study, we propose a concept of incremental fuzzy models in which fuzzy rules are aimed at compensating discrepancies resulting because of the use of a certain global yet simple model of general nature (such as e.g., a constant or linear regression). The structure of input data and error discovered through fuzzy clustering is captured in the form of a collection of fuzzy clusters, which helps eliminate (compensate) error produced by the global model. We discuss a detailed architecture of the proposed rule-based model and present its design based on an augmented version of Fuzzy C-Means (FCM). An extended suite of experimental studies offering some comparative analysis is covered as well.