Quasi type 2 fuzzy differential equations

Article type: Research Article

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

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

Correspondence: [*] Corresponding author. Alireza Akbarzadeh, Department of Mechanical Engineering, Center of Excellence on Soft Computing and Intelligent Information Processing, Ferdowsi University of Mashhad, P.O. Box: 9177948974, Mashhad, Iran. Tel.: +98 5118805011; E-mail: ali_akbarzadeh@um.ac.ir.

Abstract: In this paper, the notion of generalized differentiability is extended to quasi type 2 fuzzy mappings and the concept of quasi type 2 fuzzy derivative is defined. Then, based on this definition and by using the alpha-cut extension principle, an effective method is proposed for solving quasi type 2 fuzzy differential equations. Finally, the applicability of the proposed method is demonstrated through several examples.

Keywords: Fuzzy derivative, generalized differentiability, fuzzy differential equations, quasi type 2 fuzzy sets

DOI: 10.3233/JIFS-152470

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 551-563, 2017