Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2485

 Title: On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions Authors: Kyurkchiev, NikolayMarkov, Svetoslav Keywords: Sigmoid FunctionsCut FunctionGeneralized Cut Function of Degree P+1Step FunctionLogistic FunctionShifted Logistic FunctionUniform 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. URI: http://hdl.handle.net/10525/2485 ISSN: 1312-6555 Appears in Collections: Volume 9 Number 1

Files in This Item:

File Description SizeFormat