COMMENTS ON SOME NEW CLASSES OF SIGMOIDAL AND ACTIVATION FUNCTIONS. APPLICATIONS

In this paper we study a new class of sigmoidal functions. We will consider the possibility of approximating the function kappa(t) = {0, 0 <= t < 1 [0, 1], t = 1 by new family with respect to Hausdorff distance. Some applications in the theory of impulse technics, filter synthesis and debugging theory are given. We analyze also the "real wealth data" and "actual data to estimate the number of software residual faults" by the new sigmoid. Some visualizations of the typical emitting charts are also given. We will consider also the possibility of approximating the function v(t) = {0, -1 <= t <= -2 beta/m 1/2, -2 beta/m < t < 2 beta/m 1, 2 beta/m <= t <= 1 by the new generalized Yun's activation function. Approximating of this function is related to the analysis of electric steps and chains. Numerical examples using GAS Mathematica, illustrating our results are presented.