On a type-2 fuzzy approach to solution of second-order initial value problem

被引：3

作者：

Bayeg, Selami ^{[1
]}

Mert, Raziye ^{[2
]}

Akin, Omer ^{[3
]}

Khaniyev, Tahir ^{[4
]}

机构：

[1] Univ Turkish Aeronaut Assoc, Dept Ind Engn, Okul Sokak 11, TR-06790 Ankara, Turkey

[2] Adana Alparslan Turkes Univ Sci & Technol, Dept Software Engn, Catalan Caddesi, TR-01250 Adana, Turkey

[3] TOBB Univ Econ & Technol, Dept Math, Sogutozu Cd 43, TR-06510 Ankara, Turkey

[4] TOBB Univ Econ & Technol, Dept Ind Engn, Sogutozu Cd 43, TR-06510 Ankara, Turkey

来源：

SOFT COMPUTING | 2022年 / 26卷 / 04期

关键词：

Type-2 fuzzy second order differential equation; Perfect triangular type-2 fuzzy number; (alpha; beta)-cut representation; Mechanical vibration; RLC circuit; DIFFERENTIAL-EQUATIONS; SETS;

D O I：

10.1007/s00500-021-06607-2

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

In this paper, we have proposed a new representation of the triangular type-2 fuzzy numbers called the perfect triangular type-2 fuzzy numbers and defined their level sets by the (alpha, beta)-cut representation. With respect to this (alpha, beta)-cut representation, we have defined the algebraic operations for perfect triangular type-2 fuzzy numbers by using interval arithmetics. And then, we have proposed a method to find the solutions for second-order initial value problems with perfect triangular type-2 fuzzy initial conditions and forcing coefficients based on the Zadeh's extension principle. Finally, we have used the proposed method for the mechanical vibration and RLC circuit models with perfect triangular type-2 fuzzy numbers.

引用

页码：1671 / 1683

页数：13

共 50 条

[41] The novel approach for ranking generalized interval type-2 trapezoidal fuzzy numbers based on integral value
Sam'an, Muhammad
Dasril, Yosza
JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2022, 25 (06) : 1697 - 1711
[42] Fuzzy Initial Value Problem: A Short Survey
Mizukoshi, Marina Tuyako
FUZZY INFORMATION PROCESSING, NAFIPS 2018, 2018, 831 : 464 - 476
[43] Solving second-order nonlinear boundary value problem with nonlinear boundary conditions by an iterative method
Liu, Chein-Shan
Chang, Jiang-Ren
ENGINEERING COMPUTATIONS, 2021, 38 (01) : 107 - 130
[44] Global bifurcation of positive solutions of a second-order periodic boundary value problem with indefinite weight
Ma, Ruyun
Xu, Jia
Han, Xiaoling
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (10) : 3379 - 3385
[45] On a fractional higher order initial value problem
Souahi, A.
Guezane-Lakoud, A.
Khaldi, R.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2018, 56 (1-2) : 289 - 300
[46] A class of explicit two-step superstable methods for second-order linear initial value problems
Saldanha, Godfrey
Saldanha, Donna Jennifer
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2009, 86 (08) : 1424 - 1432
[47] Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs
Datsko, B. Y.
Kutniv, M. V.
NUMERICAL ALGORITHMS, 2025, 98 (02) : 929 - 942
[48] A Second-Order Boundary Value Problem with Nonlinear and Mixed Boundary Conditions: Existence, Uniqueness, and Approximation
Zhou, Zheyan
Shen, Jianhe
ABSTRACT AND APPLIED ANALYSIS, 2010,
[49] High order α-planes integration: A new approach to computational cost reduction of General Type-2 Fuzzy Systems
Ontiveros, Emanuel
Melin, Patricia
Castillo, Oscar
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE, 2018, 74 : 186 - 197
[50] On the Floquet problem for second-order Marchaud differential systems
Andres, Jan
Kozusnikova, Martina
Malaguti, Luisa
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 351 (01) : 360 - 372

← 1 2 3 4 5 →