On the approximation properties of fuzzy transform

Article type: Research Article

Authors: Ziari, Shokrollah^{a; *} | Perfilieva, Irina^b

Affiliations: [a] Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran | [b] University of Ostrava, Institute for Research and Applications of Fuzzy Modeling, Ostrava, Czech Republic

Correspondence: [*] Corresponding author. Shokrollah Ziari, Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran. Tel.: +989126888947; E-mail: shok_ziari@yahoo.com.

Abstract: In this paper, we continue a study of approximation properties of the fuzzy transform (F-transform) with the partition generated by the Shepard kernel. We make the error estimate in terms of a modulus of continuity which has a higher order than the previously known. Also, we obtain the error estimate of the iterative F-transform-based method for linear Fredholm integral equations of the second kind.

Keywords: Fuzzy transform, Shepard operator, Fredholm integral equations

DOI: 10.3233/JIFS-161413

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 1, pp. 171-180, 2017