Artificial neural network approach to the fuzzy Abel integral equation problem

作者：Jafarian Ahmad^*; Nia Safa Measoomy

来源：Journal of Intelligent and Fuzzy Systems, 2014, 27(1): 83-91.

DOI：10.3233/IFS-130980

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

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.

• 出版日期2014