### Interval Solutions of Interval Linear Systems

LI Haohao1, XIA Mengxue2, JIN Jianghong3

1. 1. School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou 310018;
2. Department of Basic, PLA Army Academy of Artillery and Air Defense, Hefei 230031;
3. School of science, Hangzhou Dianzi University, Hangzhou 310018
• Received:2020-12-25 Revised:2021-07-29 Published:2022-03-16

LI Haohao, XIA Mengxue, JIN Jianghong. Interval Solutions of Interval Linear Systems[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(12): 3395-3404.

The mathematical models of various uncertain systems in engineering and scientific practice can be described by interval systems and interval optimization models. In this paper, we discuss the problem of interval solutions for interval systems. We define several new interval solutions for mixed interval linear systems, including weak interval solutions, strong interval solutions, tolerance interval solution and control interval solution and study their related properties. In particular, the characterizations of weak interval solution, strong interval solution, tolerance interval solution and control interval solution of the interval equations ${\bm A}{\bm x}={\bm b}$ and the interval inequalities ${\bm A}{\bm x}\leq{\bm b}$ are established. These characterizations are similar to the classical Oettli-Prager inequality and Gerlach inequality. At the same time, we give some examples to illustrate the application background and calculation method of interval solutions.

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