Scattered data approximation of fully fuzzy data by quasi-interpolation

Document Type : Research Paper


1 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Convergent Solutions, LLC, Livermore, CA, USA.


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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