Utilizing a new feed-back fuzzy neural network for solving a system of fuzzy equations

Subject Areas : International Journal of Industrial Mathematics

A. Jafarian ¹ , S. Measoomy Nia ²

1 - Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran.
2 - Department of Mathematics, Urmia Branch, Islamic Azad University, Urmia, Iran.

Received: 2013-11-04 Accepted : 2013-11-04 Published : 2013-12-01

Keywords: System of fuzzy equations, Fuzzy feed-back neural network, Cost function, Learning algorithm,

Abstract :

This paper intends to offer a new iterative method based on articial neural networks for finding solution of a fuzzy equations system. Our proposed fuzzied neural network is a ve-layer feedback neural network that corresponding connection weights to output layer are fuzzy numbers. This architecture of articial neural networks, can get a real input vector and calculates its corresponding fuzzy output. In order to nd the approximate solution of the fuzzy system that supposedly has a real solution, rst a cost function is dened for the level sets of the fuzzy network and target output. Then a learning algorithm based on the gradient descent method is used to adjust the crisp input signals. The present method is illustrated by several examples with computer simulations.