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Scattered data approximation of fully fuzzy data by quasi-interpolation | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 16، شماره 3، مرداد و شهریور 2019، صفحه 63-72 اصل مقاله (405.43 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2019.4645 | ||
| نویسندگان | ||
| K. Shakibi* 1؛ M. Amirfakhrian1؛ E. J. Kansa2 | ||
| 1Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran | ||
| 2Convergent Solutions, LLC, Livermore, CA, USA. | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Quasi-interpolation؛ Fuzzy interpolation؛ Fuzzy logic؛ Radial basis function؛ Linear reproducing property | ||
| مراجع | ||
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