Stability in credibility for fuzzy differential equation

Article type: Research Article

Authors: You, Cuilian^{; *} | Hao, Yangyang | Su, Ke

Affiliations: College of Mathematics and Information Science, Hebei University, Baoding, China

Correspondence: [*] Corresponding author. Cuilian You, College of Mathematics and Information Science, Hebei University, Baoding 071002, China. Tel.: +8615933955927; Fax: +8603123168912; E-mail: yycclian@163.com.

Abstract: Stability plays a major role in differential equation which means sensitivity of the state of a system to small changes in the initial state. Thus, it is critically important to make stability analysis for fuzzy differential equation. This paper mainly proposed a concept of stability in credibility for fuzzy differential equation driven by Liu process. Based on this concept, some theorems for fuzzy differential equation driven by Liu process being stability in credibility were proved. Furthermore, we extended the theorems to the case of n-dimensional fuzzy differential equation driven by Liu process.

Keywords: Fuzzy differential equation, fuzzy process, Liu process, stability

DOI: 10.3233/JIFS-181150

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 1, pp. 213-218, 2019