Interval-valued fuzzy derivatives and solution to interval-valued fuzzy differential equations

Article type: Research Article

Authors: Kalani, Hadi^{a; b} | Akbarzadeh-T, Mohammad-R.^{a; c} | Akbarzadeh, Alireza^{a; b; *} | Kardan, Iman^{a; b}

Affiliations: [a] Center of Excellence on Soft Computing and Intelligent Information Processing | [b] Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran | [c] Department of Electrical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

Correspondence: [*] Corresponding author. Alireza Akbarzadeh, Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran. Tel.: +98 9155210253; E-mail: ali_akbarzadeh@um.ac.ir.

Abstract: In this paper, we define the concept of fuzzy derivatives for perfect and semi-perfect interval-valued fuzzy mappings. Based on this definition, we then present a method for solving interval-valued fuzzy differential equations using the alpha-cut extension principle. Finally, several examples are provided to demonstrate the effectiveness of the proposed method.

Keywords: Generalized differentiability, perfect and semi-perfect interval-valued fuzzy sets, fuzzy differential equations

DOI: 10.3233/IFS-162085

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 6, pp. 3373-3384, 2016