Numerical solutions for fuzzy Fredholm integral equations of the first kind using Landweber iterative method¹

Article type: Research Article

Authors: Yang, Hong^{; *} | Gong, Zengtai

Affiliations: College of Mathematics and Statistics, Northwest Normal University, Lanzhou, PR China

Correspondence: [*] Corresponding author. Hong Yang, College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, PR China. Tel.: +8613619316908; E-mail: ysin888@163.com.

Note: [1] This work is supported by National Natural Science Foundation of China (61763044) and Natural Science Foundation of Gansu Province (18JR3RA096).

Abstract:  In this paper, we proposed an iterative procedure based on Landweber iterative methods to solve fuzzy Fredholm integral equations of the first kind. In addition, this research be based on a strictly convex fuzzy number space and the Riemann integral of fuzzy-number-valued function which is taken value in the space. The error estimation of the proposed method in terms of uniform and partial modulus of continuity was given. The generalized difference of fuzzy numbers was controlled and estimated reasonably. And it was avoided to compute the generalized difference of fuzzy numbers during the iterations. Finally, two illustrative examples are included in order to demonstrate the accuracy and the convergence of the proposed method.

Keywords: Fuzzy numbers, Fuzzy Integral equation, Iterative method, Uniform modulus of continuity, Partial modulus of continuity

DOI: 10.3233/JIFS-190972

Journal: Journal of Intelligent & Fuzzy Systems, vol. 38, no. 3, pp. 3059-3074, 2020