sir entirely agree with you but mostly we used this activation function in the particular mentioned neural network. I have read in so many research paper.
May be this is also one of the reasons: The sigmoidal functions are most widely used in back propagation network because of the relationship between the value of the functions at a point and the value of the derivative at that point which reduces the computational burden during training. [as per the author S N Sivanandam & S N Deepa, "Principles of Soft Computing"]
A common choice of activation function in MLP NNs is the Sigmoid function, since it takes a real-valued input and squashes it to range between 0 and 1, i.e., it produces a curve with an “S” shape similar to TLU. Sigmoid function is differentiable often used to introduce nonlinearity in the model. A reason for its popularity is because the Sigmoid function [f=1/(1+e-x)] satisfies a property between the derivative and itself [f'=f(1-f)] such that it is computationally easy to perform.
However for RBF NNs, a RBF is a real-valued function whose value depends only on the distance from the origin, i.e., it is a function w.r.t. the origin or a certain point. Accordingly, a RBF NN often takes Gaussian function as its basis function which is symmetrical about a center maximum. Gaussians are probably the most used basis functions in RBF.
Agreed with Mahmoud Omid. Beautifully elaborated. Yes, this is to confine the possible outcome of the network between 0 and 1 (real value), while sgn (signum) is hard valued mean either 0 or 1.
I think you are talking about activation function right? If we consider BP-MLP, Back propagation (BP) is used for training multi-layers network and any activation function function you can used in hidden layers but in output layer it is suggested to keep purlin(.) only.