The α-path of multi-dimensional uncertain differential equations and its applications

Article type: Research Article

Authors: Wang, Xiaoli | Wang, Chongguo | Shi, Gang^{; *}

Affiliations: School of Computer Science and Technology, Xinjiang University, Urumqi, China

Correspondence: [*] Corresponding author. Gang Shi, School of Computer Science and Technology, Xinjiang University, Urumqi 830046, China. Email: shigang@xju.edu.cn.

Abstract: As a complex uncertain differential equation, how to solve the multi-dimensional uncertain differential equation is a complicated and difficult problem. This paper will be devoted to the α-path of some special multi-dimensional uncertain differential equations, namely, multi-factor uncertain differential equations, nested uncertain differential equations and multi-factor nested uncertain differential equations. The α-path method is used to study the numerical solution problems of the above three special multi-dimensional uncertain differential equations. At the same time, the inverse uncertainty distributions and expected values of these three special multi-dimensional uncertain differential equations are also obtained. At last, the numerical algorithm examples are given to verify it.

Keywords: Uncertainty theory, multi-dimensional uncertain differential equation, α-path, numerical algorithm

DOI: 10.3233/JIFS-234432

Journal: Journal of Intelligent & Fuzzy Systems, vol. 46, no. 2, pp. 4761-4776, 2024