Bivariate fully fuzzy interpolation problem using artificial neural networks approach

Article type: Research Article

Authors: Hosseini, E. | Jafarian, A.^*

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

Correspondence: [*] Corresponding author. A. Jafarian, Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran. Tel./Fax: +98 4433662872; E-mail: jafarian5594@yahoo.com.

Abstract: Artificial neural networks modeling is one of the most prominent techniques for solving more complicated mathematical problems that can not be solved in the traditional computing environments. The work described here intends to offer an efficient bivariate fuzzy interpolation methodology based on the artificial neural networks approach. It has several notable features including high processing speeds and the ability to learn the solution to a problem from a set of examples which categorizes them in line of intelligent systems. To do this, a multilayer feed-forward neural architecture is depicted for constructing a fully fuzzy interpolating polynomial of arbitrary degree. Then, a back-propagation supervised learning optimization algorithm will be applied for estimating the unknown fuzzy coefficients of the solution polynomial. Finally, the advantage of our technique is illustrated by using some practical examples to show the ability of the improved algorithm in solving rigorous problems.

Keywords: Bivariate fully fuzzy polynomial, artificial neural network, approximate solution, criterion function, learning algorithm

DOI: 10.3233/IFS-151996

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 4, pp. 2267-2275, 2016