Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
Fuzzy Neural Networks with Fuzzy Weights
Hisao ISHIBUCHIHidehiko OKADAHideo TANAKA
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1993 Volume 6 Issue 3 Pages 137-148

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Abstract

In this paper, we first propose an architecture of neural networks that have fuzzy weights and fuzzy biases. A neural network with the proposed architecture maps an input vector of real numbers to an output of fuzzy number. Therefore the neural network can be viewed as an approximator of non-linear fuzzy functions from real vectors to fuzzy numbers. Next we define a cost function using the fuzzy output from the neural network and the corresponding fuzzy target output. A learning algorithm can be derived from the cost function in a similar manner as the BP (Back-Propagation) algorithm. We also define two variations of the cost function that are based on the inclusion relation between the fuzzy output and the fuzzy target. Two learning algorithms can be also derived from the two cost functions. The derived learning algorithms are illustrated by computer simulations for numerical examples.

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