The Parameter Estimation And Prediction Of The Linear Regression Model Based On LR-fuzzy Numbers

The linear regression model is one of the most widely used mathematicalmodel in the mathematical statistics such as society science、natural science、engineering science and so on. Nowadays the research of the linear regressionmodel has been already perfect, but it is always limited to accurate numbers.On the one hand, the observations are fuzziness and randomness in the real lifesuch as the earthquake prediction; on the other hand, the LR-fuzzy number is avery important kind of fuzzy numbers. In this case, we discuss the parameterestimation of the fuzzy linear regression model; we focus on studying thefuzzy optimal linear unbiased prediction and the fuzzy simple projectionprediction of the fuzzy linear prediction model based on LR-fuzzy numbers.This paper includes6chapters. The analysis of the fuzzy regression modeland the classical optimal prediction in finite populations are introduced, andthen we come up with the working plan in chapter2. As the basis of this paper,we recommend the relevant knowledge of LR-fuzzy numbers and the inverse ofthe matrix; especially when the fuzzy number is random variable, we give theexpression forms with expectation and variance in chapter2.we study theparameter estimation of the fuzzy linear regression model with accurate inputsand fuzzy outputs In chapter3; specifically, we study the parameter estimationof the fuzzy linear regression model with fuzzy linear constraint conditions. Inchapter4, we discuss the fuzzy optimal linear unbiased prediction and the fuzzyoptimal linear unbiased prediction with fuzzy linear constraint conditions of thefuzzy linear prediction model based on LR type symmetric fuzzy numbers. Weget the fuzzy simple projection prediction with LR type symmetric fuzzycoefficients in chapter5.The fuzzy linear regression model solves the problem it is the way to buildthe model when observations are fuzziness and randomness in the real life. Weget the parameter estimation of the fuzzy linear regression model based on LR-fuzzy coefficients and then we obtain the conclusion of fuzzy optimal linearunbiased prediction of the fuzzy linear prediction model based on LR-fuzzycoefficients. Compared with the parameter estimation and the prediction of theclassical linear model, the processing method in the paper can be statisticallyanalyzed and we get better statistical properties.