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Journal Paper

Scattered Data Approximation of Fully Fuzzy Data by Quasi-interpolation

Iranian Journal of Fuzzy Systems, Vol. 16, No. 3, (2019), 63-72.

Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $\widetilde{f}^{*}:\mathbb{R}\rightarrow F(\mathbb{R})$ or $\widetilde{f}^{*}:F(\mathbb{R})\rightarrow \mathbb{R}$.  In this paper, we intend to offer a novel fuzzy radial basis function by the concept of source distance. Then, we will construct a fuzzy linear combination of such basis functions in order to introduce a fully fuzzy quasi-interpolation in the form of $\widetilde{f}^{*}:F(\mathbb{R})\rightarrow F(\mathbb{R})$. Also the error estimation of the proposed method is proved in terms of the fully fuzzy modulus of continuity which will be introduced in this paper. Finally some examples have been given to emphasize the acceptable accuracy of our method.

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Journal Paper

Fuzzy Quasi-Interpolation Solution for Fredholm Fuzzy Integral Equations of Second Kind

Soft Computing, Vol. 21, No. 15, (2017) 4323–4333.

In this paper, we intend to offer a new approach to solve Fredholm fuzzy integral equation of the second kind by the concept of source distance and fuzzy quasi-interpolation. The error estimation of the proposed method is proved in terms of the fuzzy modulus of continuity which will be introduced in this paper. Finally some examples have been given to emphasize acceptable accuracy of our method.

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Journal Paper

Solving Integro-Differential Equation by Using B-Spline Interpolation

International Journal of Mathematical Modelling & Computations, Vol. 3 No. 3, (2013) 237– 244.

In this paper a numerical technique based on the B-spline method is presented for the solution of Fredholm integro-differential equations. To illustrate the efficiency of the method some examples are introduced and the results are compared with the exact solution.

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