Numerical Solution of Fuzzy Partial Differential Equations by Using Modified Fuzzy Neural Networks

A.Hussian, Eman; Suhhiem, Mazin H.

doi:10.9734/bjmcs/2016/20504

Cited by 11 publications

(13 citation statements)

References 21 publications

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“…In [45] a modified technique is proposed in order to obtain the numerical solutions of fuzzy PDEs by utilizing fuzzy artificial neural networks. Utilizing modified fuzzy neural network ensures that the training points get selected over an open interval without training the network in the range of first and end points.…”

Section: Neural Network Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Fuzzy Control of Uncertain Nonlinear Systems with Numerical Techniques: A Survey

Jafari

Razvarz

Gegov

et al. 2019

Advances in Intelligent Systems and Computing

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This paper provides an overview of numerical methods in order to solve fuzzy equations (FEs). It focuses on different numerical methodologies to solve FEs, dual fuzzy equations (DFEs), fuzzy differential equations (FDEs) and partial fuzzy differential equations (PFDEs). The solutions which are produced by these equations are taken to be the controllers. This paper also analyzes the existence of the roots of FEs and some important implementation problems. Finally, several examples are reviewed with different methods.

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Section: Neural Network Methodsmentioning

confidence: 99%

“…In [46] a novel technique on the basis of learning algorithm associated with the fuzzy neural network as well as Taylor series is laid down for extracting numerical solution of FDEs. A fuzzy neural network on the basis of the semi-Taylor series (in concerned to the function e x ) for the first (and second) order FDE is utilized.…”

Section: Neural Network Methodsmentioning

confidence: 99%

Fuzzy Control of Uncertain Nonlinear Systems with Numerical Techniques: A Survey

Jafari

Razvarz

Gegov

et al. 2019

Advances in Intelligent Systems and Computing

View full text Add to dashboard Cite

show abstract

“…In [32] a modified technique is proposed in order to obtain the numerical solutions of fuzzy PDEs by utilizing fuzzy artificial neural networks. Utilizing modified fuzzy neural network ensures that the training points get selected over an open interval without training the network in the range of first and end points.…”

Section: -mentioning

confidence: 99%

Fuzzy Differential Equations for Modeling and Control of Fuzzy Systems

Jafari

Razvarz

Gegov

2018

13th International Conference on Theory and Application of Fuzzy Systems and Soft Computing — ICAFS-2018

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A survey of the methodologies associated with the modeling and control of uncertain nonlinear systems has been given due importance in this paper. The basic criteria that highlights the work is relied on the various patterns of techniques incorporated for the solutions of fuzzy differential equations (FDEs) that corresponds to fuzzy controllability subject. The solutions which are generated by these equations are considered to be the controllers. Currently, numerical techniques have come out as superior techniques in order to solve these types of problems. The implementation of neural networks technique is contributed in the complex way of dealing the appropriate solutions of the fuzzy systems.

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“…There is still a lack of qualitative and quantitative researches for fuzzy partial differential equations (PDEs), which were first introduced by Buckley and Feuring [18] in 1999. The available theoretical results obtained up to now for such equations may be found in [19][20][21]. The papers [22][23][24] considered the existence and uniqueness of fuzzy solutions for some fuzzy functional partial differential equations with different types of initial conditions for some classes of hyperbolic equations; almost all of the previous results were based on the Banach fixed point theorem.…”

Section: Introductionmentioning

confidence: 99%

The Existence and Uniqueness of Intuitionistic Fuzzy Solutions for Intuitionistic Fuzzy Partial Functional Differential Equations

Amma

Melliani

Chadli

2019

International Journal of Differential Equations

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In this paper, we consider intuitionistic fuzzy partial functional differential equations with local and nonlocal initial conditions using the Banach fixed point theorem. A new complete intuitionistic fuzzy metric space is proposed to investigate the existence and uniqueness of intuitionistic fuzzy solutions for these problems. We use the level-set representation of intuitionistic fuzzy functions and define the solution to an intuitionistic fuzzy partial functional differential equation problem through a corresponding parametric problem and further develop theoretical results on the existence and uniqueness of the solution. An example is presented to illustrate the results with some numerical simulation for α-cuts of the intuitionistic fuzzy solutions: we give the representation of the surface of intuitionistic fuzzy solutions.

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Numerical Solution of Fuzzy Partial Differential Equations by Using Modified Fuzzy Neural Networks

Cited by 11 publications

References 21 publications

Fuzzy Control of Uncertain Nonlinear Systems with Numerical Techniques: A Survey

Fuzzy Control of Uncertain Nonlinear Systems with Numerical Techniques: A Survey

Fuzzy Differential Equations for Modeling and Control of Fuzzy Systems

The Existence and Uniqueness of Intuitionistic Fuzzy Solutions for Intuitionistic Fuzzy Partial Functional Differential Equations

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