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Applying the Fuzzy CESTAC Method to Find the Optimal Shape Parameter in Solving Fuzzy Differential Equations via RBF-Meshless Method

Soft Computing, 2020, In Press

In this paper, by using the CESTAC method and the CADNA library a procedure is proposed to solve a fuzzy initial value problem based on RBF-meshless methods under generalized H-differentiability. So a reliable approach is presented to determine optimal shape parameter and number of points for RBF-meshless methods. The results reveal that the proposed method is very effective and simple. Also, the numerical accuracy of the method is shown in the tables and figures, and algorithms are given based on the stochastic arithmetic. The examples illustrate the efficiency and importance of using the stochastic arithmetic in place of the floating-point arithmetic.

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The use of CADNA Library to Find Optimal Shape Parameter and Optimal Number of Points in RBF-Meshless Method to Solve Differential Equations

Computational Methods for Differential Equations, 2020, In Press

One of the schemes to find the optimal shape parameter and optimal number of points in the radial basis function (RBF) methods is to apply the stochastic arithmetic (SA) in place of the common floating-point arithmetic (FPA). The main purpose of this work is to introduce a reliable approach based on this new arithmetic to compute the optimal shape parameter and number of points in multiquadric and Gaussian RBF-meshless methods for solving differential equations, in the iterative process. To this end, the CESTAC method is applied. Also, in order to implement the proposed algorithms, the CADNA library is performed. The examples illustrate the efficiency and importance of using this library to validate the results.

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A Fuzzy System Based Active Set Algorithm for the Numerical Solution of the Optimal Control Problem Governed by Partial Differential Equations

European Journal of Control, 2019, In Press

A computational indirect method based on a fuzzy system technique and active set strategy is presented. This new method has been used for the numerical solution of an optimal control problem governed by elliptic partial differential equation. To solve this problem, we start with obtaining the first-order necessary optimality conditions, which contain a mixed variational inequality in function space. Then a fuzzy basis functions technique combined with a primal-dual active set method to derive a new efficient algorithm for solving the given problem. Finally, some numerical examples are given to illustrate the accuracy and efficiency of the proposed technique.

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Application of ANNs Approach for Solving Fully Fuzzy Polynomials System

Journal of Fuzzy Set Valued Analysis, Vol. 2017 No.3 (2017) 132-142.

In processing indecisive or unclear information, the advantages of fuzzy logic and neurocomputing disciplines should be taken into account and combined by fuzzy neural networks. The current research intends to present a fuzzy modeling method using multi-layer fuzzy neural networks for solving a fully fuzzy polynomials system. To clarify the point, it is necessary to inform that a supervised gradient descent-based learning law is employed. The feasibility of the method is examined using computer simulations on a numerical example. The experimental results obtained from the investigation of the proposed method are valid and delivers very good approximation results

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New Paper

The use of CESTAC method to find optimal shape parameter and optimal number of points in RBF-meshless methods to solve differential equations

Our new paper on optimal shape parameter in Radial Basis Functions applied to differential equations. This work is a collaboration with Dr. Hassan Barzegar, Dr. M. A. Fariborzi Araghi, and me.