Uncertain hypothesis testing and its application

A common method of testing the reasonableness of estimates of unknown parameters in uncertain differential equations is to judge them by the α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-path of the differential equation. If all observations fall between the α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}-paths, the estimates are considered reasonable. This paper introduces uncertain hypothesis testing into uncertain differential equations to test the reasonableness of the estimates, which is another new approach. Further, the concept of interval estimation of unknown parameters for uncertain differential equations is introduced. Some numerical examples are given to verify the feasibility of the method. The uncertain differential equations are also used to model global average temperature data, and the results are satisfactory.