Approximate solutions of dual fuzzy polynomials by feed-back neural networks

Recently, artificial neural networks (ANNs) have been extensively studied and used in different areas such as pattern recognition, associative memory, combinatorial optimization, etc. In this paper, we investigate the ability of fuzzy neural networks to approximate solution of a dual fuzzy polynomial of the form $a_{1}x+ ...+a_{n}x^n =b_{1}x+ ...+b_{n}x^n+d,$ where $a_{j},b_{j},d epsilon E^1 (for j=1,...,n).$ Since the operation of fuzzy neural networks is based on Zadeh's extension principle. For this scope we train a fuzzified neural network by back-propagation-type learning algorithm which has five layer where connection weights are crisp numbers. This neural network can get a crisp input signal and then calculates its corresponding fuzzy output. Presented method can give a real approximate solution for given polynomial by using a cost function which is defined for the level sets of fuzzy output and target output. The simulation results are presented to demonstrate the efficiency and effectiveness of the proposed approach.