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New Artificial Intelligence Approach for Solving Fuzzy Polynomial Equations

Ahmad Jafarian

Abstract



Recently, there has been a considerable amount of interest and practice in solving many problems of several applied fields by fuzzy polynomials. In this paper, we intend to offer a new method for finding a solution of fully fuzzy polynomial with degree n, by using an artificial fuzzified feed-forward neural network. This neural net has the ability to get fuzzy vector as an input, and calculates its corresponding fuzzy output. It is clear that the input-output
relation for each unit of fuzzy neural network is defined by the extension principle of Zadeh. In this work, a cost function is also defined for the level sets of fuzzy output and fuzzy target. Then we derive a learning algorithm from the cost function for adjusting three parameters of each triangular fuzzy weight. Consequently, our approach is illustrated by computer simulations on numerical examples. It is worthwhile to mention that, the application of this
method in fluid mechanics has been shown by an example.

Keywords


Fuzzy polynomials, Fuzzy feed-forward neural networks, Learning algorithm, Cost function, Fuzzy solution.

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