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

[1] On a type-2 fuzzy approach to solution of second-order initial value problem
Selami Bayeğ
Raziye Mert
Ömer Akın
Tahir Khaniyev
Soft Computing, 2022, 26 : 1671 - 1683
[2] On the existence of a solution of a second-order singular initial value problem
Aslanov, Afgan
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (05) : 980 - 990
[3] Initial value problem for second-order random fuzzy differential equations
Ho Vu
Le Si Dong
ADVANCES IN DIFFERENCE EQUATIONS, 2015, : 1 - 23
[4] Initial value problem for second-order random fuzzy differential equations
Ho Vu
Le Si Dong
Advances in Difference Equations, 2015
[5] Existence of positive solution to a singular second-order initial value problem with impulses
Li, Jianli
Shen, Jianhua
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 206 (02) : 699 - 712
[6] On The Solvability of a Second-Order Singular Initial Value Problem
Kelevedjiev, P.
Popivanov, N.
Bekesheva, L.
APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE'14), 2014, 1631 : 245 - 254
[7] Second-order initial value problems of singular type
Agarwal, RP
O'Regan, D
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 229 (02) : 441 - 451
[8] An Efficient Method for Solving Second-Order Fuzzy Order Fuzzy Initial Value Problems
Dallashi, Qamar
Syam, Muhammed I.
SYMMETRY-BASEL, 2022, 14 (06):
[9] An algorithm for the solution of second order fuzzy initial value problems
Akin, O.
Khaniyev, T.
Oruc, O.
Turksen, I. B.
EXPERT SYSTEMS WITH APPLICATIONS, 2013, 40 (03) : 953 - 957
[10] Initial value problems in Type-2 fuzzy environment
Mohapatra, Dhabaleswar
Chakraverty, S.
MATHEMATICS AND COMPUTERS IN SIMULATION, 2023, 204 : 230 - 242

← 1 2 3 4 5 →