A Review on Fuzzy Differential Equations

• Main Authors: Mehran Mazandarani, Li Xiu
• Format: Article
• Language: English
• Published: IEEE 2021-01-01
• Series: IEEE Access
• Subjects: Fuzzy numbers; fuzzy derivatives; Hukuhra difference; granular differentiability; fuzzy mathematics; fuzzy number-valued functions
• Online Access: https://ieeexplore.ieee.org/document/9408628/

Since the term “Fuzzy differential equations” (FDEs) emerged in the literature in 1978, prevailing research effort has been dedicated not only to the development of the concepts concerning the topic, but also to its potential applications. This paper presents a chronological survey on fuzzy differential equations of integer and fractional orders. Attention is concentrated on the FDEs in which a definition of fuzzy derivative of a fuzzy number-valued function has been taken into account. The chronological rationale behind considering FDEs under each concept of fuzzy derivative is highlighted. The pros and cons of each approach dealing with FDEs are also discussed. Moreover, some of the proposed FDEs applications and methods for solving them are investigated. Finally, some of the future perspectives and challenges of fuzzy differential equations are discussed based on our personal view point.