A Review on Fuzzy Differential Equations

被引：55

作者：

Mazandarani, Mehran ^{[1
]}

Xiu, Li ^{[1
]}

机构：

[1] Tsinghua Shenzhen Int Grad Sch, Dept Informat Sci & Technol, Shenzhen 518055, Peoples R China

来源：

IEEE ACCESS | 2021年 / 9卷

基金：

中国国家自然科学基金;

关键词：

Differential equations; Fuzzy sets; Switches; Mathematical model; Licenses; Fuzzy logic; Uncertainty; Fuzzy numbers; fuzzy derivatives; Hukuhra difference; granular differentiability; fuzzy mathematics; fuzzy number-valued functions; INTERVAL-VALUED FUNCTIONS; BOUNDARY-VALUE-PROBLEMS; GENERALIZED HUKUHARA DIFFERENTIABILITY; INITIAL-VALUE PROBLEM; FIXED-POINT THEOREM; RUNGE-KUTTA METHOD; NUMERICAL-SOLUTIONS; GRANULAR DIFFERENTIABILITY; SEMILINEAR SPACES; CONTROLLED SYSTEM;

D O I：

10.1109/ACCESS.2021.3074245

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：62195 / 62211

页数：17

共 218 条

[1] Tuning of reachable set in one dimensional fuzzy differential inclusions [J].

Abbasbandy, S ;

Nieto, JJ ;

Alavi, M .

CHAOS SOLITONS & FRACTALS, 2005, 26 (05) :1337-1341

[2]

Abbasbandy S., 2002, Computational Methods in Applied Mathematics, V2, DOI 10.2478/cmam-2002-0006

[3] Some new performance definitions of second-order fuzzy systems [J].

Abbasi, Seyed Mohammad Mehdi ;

Jalali, Aliakbar .

SOFT COMPUTING, 2020, 24 (06) :4109-4120

[4] A novel approach for solving fully fuzzy linear systems and their duality [J].

Abbasi, Seyed Mohammad Mehdi ;

Jalali, Aliakbar .

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2019, 37 (02) :2609-2619

[5] Fuzzy tracking control of fuzzy linear dynamical systems [J].

Abbasi, Seyed Mohammad Mehdi ;

Jalali, Aliakbar .

ISA TRANSACTIONS, 2020, 97 :102-115

[6] On conformable fractional calculus [J].

Abdeljawad, Thabet .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 279 :57-66

[7] On the linear fuzzy model associated with Caputo-Fabrizio operator [J].

Abdollahi, R. ;

Khastan, A. ;

Nieto, J. J. ;

Rodriguez-Lopez, R. .

BOUNDARY VALUE PROBLEMS, 2018,

[8] Fuzzy conformable fractional differential equations: novel extended approach and new numerical solutions [J].

Abu Arqub, Omar ;

Al-Smadi, Mohammed .

SOFT COMPUTING, 2020, 24 (16) :12501-12522

[9] Numerical solutions of fuzzy differential equations using reproducing kernel Hilbert space method [J].

Abu Arqub, Omar ;

AL-Smadi, Mohammed ;

Momani, Shaher ;

Hayat, Tasawar .

SOFT COMPUTING, 2016, 20 (08) :3283-3302

[10] A survey on fuzzy fractional differential and optimal control nonlocal evolution equations [J].

Agarwal, Ravi P. ;

Baleanu, Dumitru ;

Nieto, Juan J. ;

Torres, Delfim F. M. ;

Zhou, Yong .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2018, 339 :3-29

← 1 2 3 4 5 6 7 8 9 10 →