Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks

被引:17
|
作者
Jafari, Raheleh [1 ]
Yu, Wen [1 ]
Li, Xiaoou [2 ]
Razvarz, Sina [1 ]
机构
[1] IPN Natl Polytech Inst, CINVESTAV, Dept Control Automat, Mexico City, DF, Mexico
[2] IPN Natl Polytech Inst, CINVESTAV, Dept Computac, Mexico City, DF, Mexico
关键词
Fuzzy differential equations; Bernstein neural networks; Z-numbers; Uncertain nonlinear systems; GENERALIZED DIFFERENTIABILITY; UNCERTAINTY GTU; POLYNOMIALS; SYSTEMS;
D O I
10.2991/ijcis.10.1.81
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
The uncertain nonlinear systems can be modeled with fuzzy equations or fuzzy differential equations (FDEs) by incorporating the fuzzy set theory. The solutions of them are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by two types of Bernstein neural networks. Here, the uncertainties are in the sense of Z-numbers. Initially the FDE is transformed into four ordinary differential equations (ODEs) with Hukuhara differentiability. Then neural models are constructed with the structure of ODEs. With modified back propagation method for Z-number variables, the neural networks are trained. The theory analysis and simulation results show that these new models, Bernstein neural networks, are effective to estimate the solutions of FDEs based on Z-numbers.
引用
收藏
页码:1226 / 1237
页数:12
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