Solving linear Fredholm fuzzy integral equations of the second kind by artificial neural networks | Zendy

Hadi Hosseini Fadravi | Zendy; R. Buzhabadi | Zendy; Hassan Saberi Nik | Zendy

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Solving linear Fredholm fuzzy integral equations of the second kind by artificial neural networks

Author(s) -

Hadi Hosseini Fadravi,

R. Buzhabadi,

Hassan Saberi Nik

Publication year - 2014

Publication title -

alexandria engineering journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.584

H-Index - 58

eISSN - 2090-2670

pISSN - 1110-0168

DOI - 10.1016/j.aej.2013.12.002

Subject(s) - fredholm integral equation , integral equation , mathematics , fuzzy logic , robustness (evolution) , fredholm theory , artificial neural network , integral transform , parametric statistics , mathematical optimization , mathematical analysis , computer science , artificial intelligence , biochemistry , chemistry , statistics , gene

This paper deals with the solutions of fuzzy Fredholm integral equations using neural networks. Based on the parametric form of a fuzzy number, a Fredholm fuzzy integral equation converts to two systems of integral equations of the second kind in the crisp case. This method employs a growing neural network as the approximate solution of the integral equations, for which the activation functions are log-sigmoid and linear functions. The parameters of the approximate solution are adjusted by using an unconstrained optimization problem. In order to show this capability and robustness, some fuzzy Fredholm integral equations are solved in detail as numerical examples

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