On the Approximation of the Generalized Cut Function of Degree p+1 By Smooth Sigmoid Functions
Nikolay V. Kyurkchiev, Svetoslav Marinov Markov · Serdica Journal of Computing · 2015
We introduce a modification of the familiar cut function byreplacing the linear part in its definition by a polynomial of degree p + 1obtaining thus a sigmoid function called generalized cut function of degreep + 1 (GCFP). We then study the uniform approximation of the (GCFP)by smooth sigmoid functions such as the logistic and the shifted logisticfunctions. The limiting case of the interval-valued Heaviside step functionis also discussed which imposes the use of Hausdorff metric. Numericalexamples are presented using CAS MATHEMATICA.