Please use this identifier to cite or link to this item: https://doi.org/10.1109/72.536310
Title: The min-max function differentiation and training of fuzzy neural networks
Authors: Zhang, X.
Hang, C.-C. 
Tan, S. 
Wang, P.-Z. 
Issue Date: 1996
Source: Zhang, X., Hang, C.-C., Tan, S., Wang, P.-Z. (1996). The min-max function differentiation and training of fuzzy neural networks. IEEE Transactions on Neural Networks 7 (5) : 1139-1150. ScholarBank@NUS Repository. https://doi.org/10.1109/72.536310
Abstract: This paper discusses the Δ-rule and training of min-max neural networks by developing a differentiation theory for min-max functions, the functions containing min (∧) and/or max (∨) operations. We first prove that under certain conditions all min-max functions are continuously differentiable almost everywhere in the real number field R-fraktur sign and derive the explicit formulas for the differentiation. These results are the basis for developing the Δ-rule for the training of min-max neural networks. The convergence of the new Δ-rule is proved theoretically using the stochastic theory, and is demonstrated with a simulation example. © 1996 IEEE.
Source Title: IEEE Transactions on Neural Networks
URI: http://scholarbank.nus.edu.sg/handle/10635/62861
ISSN: 10459227
DOI: 10.1109/72.536310
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