Neural Networks with Interval Weights for Nonlinear Mappings of Interval Vectors

Kitaek KWON  Hisao ISHIBUCHI  Hideo TANAKA  

IEICE TRANSACTIONS on Information and Systems   Vol.E77-D   No.4   pp.409-417
Publication Date: 1994/04/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Issue on Neurocomputing)
Category: Mapping
interval arithmetic,  nonlinear mapping of interval vectors,  feedforward neural networks,  back-propagation algorithm,  

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This paper proposes an approach for approximately realizing nonlinear mappings of interval vectors by interval neural networks. Interval neural networks in this paper are characterized by interval weights and interval biases. This means that the weights and biases are given by intervals instead of real numbers. First, an architecture of interval neural networks is proposed for dealing with interval input vectors. Interval neural networks with the proposed architecture map interval input vectors to interval output vectors by interval arithmetic. Some characteristic features of the nonlinear mappings realized by the interval neural networks are described. Next, a learning algorithm is derived. In the derived learning algorithm, training data are the pairs of interval input vectors and interval target vectors. Last, using a numerical example, the proposed approach is illustrated and compared with other approaches based on the standard back-propagation neural networks with real number weights.