Artificial neural network approach to the fuzzy Abel integral equation problem

Article type: Research Article

Authors: Jafarian, Ahmad | Nia, Safa Measoomy

Affiliations: Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran

Note: [] Corresponding author. Ahmad Jafarian, Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran. E-mails: jafarian5594@yahoo.com (Ahmad Jafarian); measoomy@yahoo.com (Safa Measoomy Nia).

Abstract: Artificial neural networks (ANNs) have a large appeal to many researchers due to their feature to simulate and solve different kinds of problems that do not have algorithmic solutions. The outlined in this paper is an efficient and robust collocation method based on the ANNs and Bernstein polynomials intended for the fuzzy Abel integral equation problem. To do this, first truncated Bernstein-series polynomial of the solution function is substituted in parametric form of the given fuzzy problem. Then an architecture of ANNs namely the feed-back neural nets is designed to determine values for the unknown coefficients. Eventually, the proposed method is implemented on some numerical examples, and also is compared with an usual and classical technique.

Keywords: Fuzzy Abel integral equation, bivariate Bernstein polynomial, feed-back neural network, cost function, learning algorithm

DOI: 10.3233/IFS-130980

Journal: Journal of Intelligent & Fuzzy Systems, vol. 27, no. 1, pp. 83-91, 2014