Modified hyperbolic tangent

The modified hyperbolic tangent (mtanh or mth) is a special S-shaped function based on the hyperbolic tangent, given by

This function was proposed by Elena Soboleva (of Ukraine) as a utility function for multi-objective optimization and choice modelling in decision-making.

In other papers it is used for approximation of current-voltage characteristics of field-effect transistors and light-emitting diodes.

With parameters a = b = c = d = 1 the modified hyperbolic tangent function reduces to the conventional tanh(x) function, whereas for a = b = 1 and c = d = 0, the term becomes equal to sinh(x).