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Title: On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions
Authors: Kyurkchiev, Nikolay
Markov, Svetoslav
Keywords: Sigmoid Functions
Cut Function
Generalized Cut Function of Degree P+1
Step Function
Logistic Function
Shifted Logistic Function
Uniform and Hausdorff Approximation
Issue Date: 2015
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Journal of Computing, Vol. 9, No 1, (2015), 93p-104p
Abstract: We introduce a modification of the familiar cut function by replacing the linear part in its definition by a polynomial of degree p + 1 obtaining thus a sigmoid function called generalized cut function of degree p + 1 (GCFP). We then study the uniform approximation of the (GCFP) by smooth sigmoid functions such as the logistic and the shifted logistic functions. The limiting case of the interval-valued Heaviside step function is also discussed which imposes the use of Hausdorff metric. Numerical examples are presented using CAS MATHEMATICA.
ISSN: 1312-6555
Appears in Collections:Volume 9 Number 1

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