Solving fully fuzzy polynomials using feed-back neural networks

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 have designed an artificial fuzzified feed-back neural network. With this design, we are able to find a solution of fully fuzzy polynomial with degree n. This neural network can get a 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. Next a learning algorithm based on the gradient descent method will be defined that can adjust the fuzzy connection weights. Finally, our approach is illustrated by computer simulations on numerical examples. It is worthwhile to mention that application of this method in fluid mechanics has been shown by an example.

Keywords:

• fully fuzzy polynomials
• fuzzy feed-forward neural networks
• fuzzy feed-back neural networks
• learning algorithm
• cost function

2010 AMS Subject Classifications::

• 03E72
• 92B20
• 04A72