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Journal Paper

Application of Radial Basis Functions in Solving Fuzzy Integral Equations

Neural Computing and Applications, Vol. 31, (2019), 6373–6381.

In the present paper, a numerical method based on radial basis functions (RBFs) is proposed to approximate the solution of fuzzy integral equations. By applying RBF in fuzzy integral equation, a linear system ΨC=G is obtained. Then target function would be approximated by defining coefficient vector C. Error estimation of the method has been shown which is based on exponential convergence rates of RBFs. Finally, validity of the method is illustrated by some examples.

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Journal Paper

The Application of Fuzzy Systems to Approximate the Solutions of a Nonlinear System of Equations

Bulletin of the Georgian National Academy of Sciences, Vol. 10, No. 3, (2016) 33-44.

In this paper, systems of nonlinear equations are considered to solve. To approximate the solution we are interested in combining both fuzzy systems and iterative methods. The elementary properties of the designed fuzzy system are given. To design fuzzy systems we used a singleton fuzzifier and center average defuzzifier. The proposed method overcomes the difficulties arising in calculating a complicated system of nonlinear equations using different iterative methods. To show the accuracy of the method, we apply it to some examples including some types of nonlinear systems of equations.

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Journal Paper

A New Method to Solve One and Two-Dimensional Wave Equations with Uncertainty

Journal of Computational and Theoretical Nanoscience, vol. 13, No. 8, 5021-5030.

In this paper, we propose a new method to approximate the solution of wave equations under fuzzy environment. To this purpose, we determine the uncertainties of fuzzy wave equation based on allocating method that leads to two partial differential equations (PDEs) which are placed in their defined boundary conditions. The convergence of the propose method is investigated. Finally, to assess the robustness of fuzzy wave equations various computational experiments are carried out.

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Journal Paper

Numerical Solution of Sylvester Matrix Equations: Application to Dynamical Systems

Journal of Interpolation and Approximation in Scientific Computing, Vol. 2016, SI. 1, (2016) 1-13.

In this paper a numerical algorithm for solving a fuzzy linear system of equations (FLS) is considered. This system would be changed into an optimization problem which is based on Particle Swarm optimization (PSO) algorithm. The efficiency of algorithm is illustrated by some numerical examples.

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Journal Paper

Numerical Solution of a Fuzzy Linear System by Using PSO Method

Journal of Fuzzy Set Valued Analysis, Vol. 2016, SI.1, (2016) 1-7.

In this paper a numerical algorithm for solving a fuzzy linear system of equations (FLS) is considered. This system would be changed into an optimization problem which is based on Particle Swarm optimization (PSO) algorithm. The efficiency of algorithm is illustrated by some numerical examples.

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conference paper

Application of Homotopy Perturbation Method to Fuzzy Nonlinear Klein-Gordon Equation with Variable Coefficients

13th Iranian Conference on Fuzzy Systems (IFSC), (2013) Qazvin, Iran.

In this paper, the author will first propose fuzzy nonlinear Klein-Gordon equation and then an application of He’s homotopy perturbation method is applied to solve this equation via the same strategy as Buckley- Feuring solution and Seikkala solution. Numerical illustrations that include fuzzy nonlinear Klein-Gordon equations are investigated to show the effectiveness and convenience of the method.

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