Alternative views on fuzzy numbers and their application to fuzzy differential equations

被引：0
作者：
Borzabadi, Akbar H. [1 ]
Heidari, Mohammad [2 ]
Torres, Delfim F. M. [3 ]
机构：
[1] Univ Sci & Technol Mazandaran, Dept Math, Behshahr, Iran
[2] Islamic Azad Univ, Ayatollah Amoli Branch, Young Researchers & Elite Club, Amol, Iran
[3] Univ Aveiro, Ctr Res & Dev Math & Applicat CIDMA, Dept Math, P-3810193 Aveiro, Portugal
来源：
JOURNAL OF MATHEMATICAL MODELING | 2024年 / 12卷 / 04期
关键词：
Parametric representation of fuzzy numbers; fuzzy valued functions; fuzzy differential equations; INTERVAL-VALUED FUNCTIONS; PARAMETRIC REPRESENTATION;
D O I：
10.22124/JMM.2024.26277.2325
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider fuzzy valued functions from two parametric representations of alpha-level sets. New concepts are introduced and compared with available notions. Following the two proposed approaches, we study fuzzy differential equations. Their relation with Zadeh's extension principle and the generalized Hukuhara derivative is discussed. Moreover, we prove existence and uniqueness theorems for fuzzy differential equations. Illustrative examples are given.
引用
收藏
页码：623 / 654
页数：32
相关论文
共 50 条
  • [1] On fuzzy differential equations in the quotient space of fuzzy numbers
    Qiu, Dong
    Zhang, Wei
    Lu, Chongxia
    FUZZY SETS AND SYSTEMS, 2016, 295 : 72 - 98
  • [2] Fuzzy differential equations via representation method of fuzzy numbers and fuzzy differential inclusions
    Satomi, N
    Saito, S
    8TH WORLD MULTI-CONFERENCE ON SYSTEMICS, CYBERNETICS, AND INFORMATICS, VOL XVI, PROCEEDINGS, 2004, : 486 - 490
  • [3] On some topics of fuzzy differential equations and fuzzy optimization problems via a parametric representation of fuzzy numbers
    Saito, S
    CONTEMPORARY DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2004, : 49 - 66
  • [4] On the stability of solutions of fuzzy differential equations in the quotient space of fuzzy numbers
    Qiu, Dong
    Dong, Rongwen
    Lu, Chongxia
    Mu, Chunlai
    JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, 2016, 31 (01) : 45 - 54
  • [5] Fuzzy differential equations without fuzzy convexity
    Kloeden, Peter E.
    Lorenz, Thomas
    FUZZY SETS AND SYSTEMS, 2013, 230 : 65 - 81
  • [6] A Review on Fuzzy Differential Equations
    Mazandarani, Mehran
    Xiu, Li
    IEEE ACCESS, 2021, 9 : 62195 - 62211
  • [7] A note on fuzzy differential equations
    Kaleva, O
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (05) : 895 - 900
  • [8] Revisiting fuzzy differential equations
    Bhaskar, TG
    Lakshmikantham, V
    Devi, V
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 58 (3-4) : 351 - 358
  • [9] Set differential equations versus fuzzy differential equations
    Laksmikantham, V
    APPLIED MATHEMATICS AND COMPUTATION, 2005, 164 (02) : 277 - 294
  • [10] Simulation and evaluation of fuzzy differential equations by fuzzy neural network
    Mosleh, Maryam
    Otadi, Mahmood
    APPLIED SOFT COMPUTING, 2012, 12 (09) : 2817 - 2827
12345