A new uncertain regression model and its application

Wang, Xiaosheng; Li, Haiyan; Guo, Haiying

doi:10.1007/s00500-019-03938-z

Cited by 10 publications

(5 citation statements)

References 23 publications

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“…This example uses the data designed by Wang and Guo [27] to study the relationship between the added value of industrial enterprises and the demand for industrial water. ( 1,2, ,11) i X i =  represents the added value of industrial enterprises, and  =( , , )…”

Section: Example 5: Example In Real Lifementioning

confidence: 99%

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Estimation of parameters for two-stage mixed fuzzy linear regression models

Zhang

2023

International Conference on Pure, Applied, and Computational Mathematics (PACM 2023)

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Combining nonlinear programming and least squares method, this paper proposes a two-stage mixed fuzzy linear regression model based on distance criterion. In order to ensure that the error of fuzzy estimated value and fuzzy observation value can be reduced when the explanatory variable is a clear number, the fuzzy regression model has a fuzzy adjustment term in addition to the clear regression coefficient. Firstly, based on the distance criterion, a nonlinear programming model is established to obtain the regression coefficient of the explanatory variables, and the fuzzy adjustment term is obtained based on the distance criterion and the least square method. Compared with the existing methods that cannot determine the sign of the coefficient, the method can accurately determine the sign of the regression coefficient. Finally, it is verified that the model has smaller mean square error and higher reliability than other models through a large number of numerical experiments and practical examples.

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Section: Example 5: Example In Real Lifementioning

confidence: 99%

“…Y Y Y Y represents industrial water consumption (observation data are in Table 1 in [27]). The dataset was used for the proposed TM model and the WG model established by Wang and Guo [26] to obtain the following model According to the performance index, Table 6 shows the MSE and MPF of the above model.…”

Section: Example 5: Example In Real Lifementioning

confidence: 99%

Estimation of parameters for two-stage mixed fuzzy linear regression models

Zhang

2023

International Conference on Pure, Applied, and Computational Mathematics (PACM 2023)

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“…We forecast the data according to the URELCFM III and obtained the confidence interval. We assumed that x ∼ L (17,19) is a new imprecise form of data, and we take the confidence level to be α = 95%. According to References [25], the forecast value and confidence interval were obtained as shown in Table 4.…”

Section: Numerical Examplementioning

confidence: 99%

“…Uncertainty statistics mainly include uncertain regression equation, uncertain estimation and uncertain hypothesis testing. Based on the keen interest in uncertain regression equations, many uncertain regression models have been proposed by experts and scholars [14][15][16][17][18]. Yao and Liu [19] proposed the least squares estimation to solve the unknown parameters of the uncertain regression equation.…”

Section: Introductionmentioning

confidence: 99%

Relative Error Linear Combination Forecasting Model Based on Uncertainty Theory

Hong-mei¹,

Wang²,

Wang³

et al. 2023

Symmetry

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The traditional combination forecasting model has good forecasting effect, but it needs precise historical data. In fact, many random events are uncertain, and much of the data are imprecise; sometimes, historical data are lacking. We need to study combination forecasting problems by means of uncertainty theory. Uncertain least squares estimation is an important technique of uncertain statistics, an important way to deal with imprecise data, and one of the best methods to solve the unknown parameters of uncertain linear regression equations. On the basis of the traditional combination forecasting method and uncertain least squares estimation, this paper proposes two kinds of uncertain combination forecasting models, which are the unary uncertain linear combination forecasting model and the uncertain relative error combination forecasting model, respectively. We set up several piecewise linear regression models according to the data of different periods and, according to certain weights, These piecewise linear regression models are combined into a unary uncertain linear combination forecasting model with a better forecasting effect. The uncertain relative error combination forecasting model is a new forecasting model that combines the traditional relative error linear forecasting model and the uncertain least squares estimation. Compared with the traditional forecasting model, the model can better deal with the forecasting problem of imprecise data. We verify the feasibility of the uncertain combination forecasting model through a numerical example. According to the data analysis, compared with the existing model, the forecasting effect of the proposed model is better.

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“…In 2018, Yao and Liu [15] proposed least squares estimates for unknown parameters of uncertain regression equations and Lio and Liu [16] further suggested an approach to estimate the uncertainty distribution of the disturbance term in an uncertain regression model. In 2020, Wang, Li and Guo [17] proposed a new uncertain regression model and Liu, Yang [18] proposed the least absolute deviation estimation for uncertain regression with imprecise observations. Wang et al [19,20] proposed new uncertain linear regression models.…”

Section: Introductionmentioning

confidence: 99%

Robust Total Least Squares Estimation Method for Uncertain Linear Regression Model

Shi,

Zhang,

Gao

et al. 2023

Mathematics

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In data analysis and modeling, least squares and total least squares are both mathematical optimization techniques. It is noteworthy that both the least squares method and the total least squares method are used to deal with precise and random data. However, when the given data are not random, or when the data are imprecise, and only the range of the data is available, the traditional linear regression method cannot be used. This paper presents an uncertain total least squares estimation method and an uncertain robust total least squares linear regression method based on uncertainty theory and total least squares method. The uncertain total least squares estimation can fully consider errors in the given data and the uncertain robust total least squares linear regression method can effectively eliminate outliers in the data. It is possible to obtain a more reasonable fitting effect with both of these methods, as well as to solve the predicted value and the confidence interval with these two methods. In terms of robust total least squares linear regression estimation, both uncertain total least squares regression estimation and uncertain robust total least squares regression estimation are feasible based on numerical examples. There are more accurate fitting equations and more reliable results with uncertain robust least squares linear regression estimation.

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A new uncertain regression model and its application

Cited by 10 publications

References 23 publications

Estimation of parameters for two-stage mixed fuzzy linear regression models

Estimation of parameters for two-stage mixed fuzzy linear regression models

Relative Error Linear Combination Forecasting Model Based on Uncertainty Theory

Robust Total Least Squares Estimation Method for Uncertain Linear Regression Model

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