### A reliable method to determine the ill-condition functions using stochastic arithmetic.

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In this paper, an architecture of fuzzy neural networks is proposed to find a real root of a dual fuzzy polynomial (if exists) by introducing a learning algorithm. We proposed a learning algorithm from the cost function for adjusting of crisp weights. According to fuzzy arithmetic, dual fuzzy polynomials can not be replaced by a fuzzy polynomials, directly. Finally, we illustrate our approach by numerical examples.

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