A new uncertain regression model and its application

Uncertain linear regression (ULR) model based on symmetric triangular uncertain set has been studied early. This paper extends the symmetric triangular uncertain coefficients to asymmetric triangular uncertain coefficients and builds two methods for estimating the parameters of ULR model. Our aim is to minimize the differences of the uncertain membership functions between the observed and estimated values. Firstly, we propose a linear programming method, whose principle is to minimize the sum of the absolute values of the differences between left width and right width of two triangular uncertain sets for each index i. Secondly, we develop a new nonlinear programming method by maximizing the overlaps of acreage of the estimated and real triangular uncertain sets in a particular hi\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h_i$$\end{document}-cut. Then, a criterion is established to evaluate the performance of the proposed approaches. Finally, we use an example based on industrial water demand data of China to illustrate our proposed approaches which are reasonable and compare the explanatory power of the ULR model and traditional linear regression (TLR) model using the presented evaluation criteria, which shows that the performance of the ULR model is obviously better than the TLR model.