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An architecture of neural networks with interval weights and its application to fuzzy regression analysis. (English) Zbl 0790.62072
Summary: We first propose an architecture of neural networks that have interval weights and interval biases. A neural network with the proposed architecture maps an input vector of real numbers to an output interval. The target output is also given as an interval. Next we define a cost function using the interval output from the neural network and the corresponding target output. A learning algorithm is derived from the cost function in a similar manner as the back propagation algorithm. We also show two variations of the learning algorithm for the proposed architecture, which lead to the inclusion relation between the interval output and the interval target. Last we apply the learning algorithms to fuzzy regression analysis where target outputs are given as fuzzy numbers.

MSC:
62J99 Linear inference, regression
62J05 Linear regression; mixed models
68T05 Learning and adaptive systems in artificial intelligence
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[1] Alefeld, G.; Herzberger, J., Introduction to interval computations, (1983), Academic Press New York
[2] Hayashi, I.; Tanaka, H., The fuzzy GMDH algorithm by possibility models and its application, Fuzzy sets and systems, 36, 245-258, (1990)
[3] Ishibuchi, H.; Tanaka, H., Regression analysis with interval model by neural networks, (), 1594-1599, Singapore
[4] Ishibuchi, H.; Tanaka, H., Fuzzy regression analysis using neural networks, Fuzzy sets and systems, 50, 257-265, (1992)
[5] Ivakhnenko, A.G., The group method of data handling - a rival of the method of stochastic approximation, Soviet automatic control, 13, 3, 43-55, (1968)
[6] Rumelhart, D.E.; Hinton, G.E.; Williams, R.J., Learning representations by back-propagating errors, Nature, 323, 533-536, (1986) · Zbl 1369.68284
[7] Tanaka, H., Fuzzy data analysis by possibilistic linear models, Fuzzy sets and systems, 24, 363-375, (1987) · Zbl 0633.93060
[8] Tanaka, H.; Ishhibuchi, H., Possibilistic regression analysis based on linear programming, (), 47-60
[9] Zadeh, L.A.; Zadeh, L.A.; Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning - I, II and III, Inf. sci., Inf. sci., Inf. sci., 9, 43-80, (1975) · Zbl 0404.68075
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