Liu B (2015) Uncertainty theory, 4th edn. Liu B (2012) Why is there a need for uncertainty theory? J Uncertain Syst 6(1):3–10 Liu B (2010) Uncertainty theory: a branch of mathematics for modeling human uncertainty. Liu B (2009) Some research problems in uncertainty theory. Liu B (2007) Uncertainty theory, 2nd edn. Lio W, Liu B (2018) Residual and confidence interval for uncertain regression model with imprecise observations. Kahneman D, Tversky A (1979) Prospect theory: an analysis of decision under risk. Guo H, Wang X, Gao Z (2017) Uncertain linear regression model and its application. J Uncertain Syst 6(4):256–262ĭepartment of mathematics (2014) Tongji University, Linear algebra, 6th edn. Soft Comput 24:16803–16809Ĭhen X, Ralescu D (2012) B-spline method of uncertain statistics with application to estimating distance. Wiley, CanadaĬhen D (2020) Tukey’s biweight estimation for uncertain regression model with imprecise observations. Numerical example show that the equation deformation method can effectively solve the unknown parameters of the uncertain linear regression equation.Ĭhatterjee S, Hadi S (2006) Regression analysis by example,4th edn. We also combine the equation deformation method with Cramer’s rule and matrix and propose the Cramer’s rule and matrix elementary transformation method to solve the unknown parameters of the uncertain linear regression equation. We first establish the equation deformation method of one-dimensional linear regression model and then extend it to the case of multiple linear regression model. On the basis of uncertainty theory, this paper presents an equation deformation method for solving unknown parameters in uncertain linear regression equations. Least squares estimation can fully consider the given data and minimize the sum of squares of residual error and can effectively solve the linear regression equation of imprecisely observed data.
When the observed data are imprecise, the uncertain regression model is more suitable for the linear regression analysis.
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