Fuzzy activation functions

The high degree complexity of the features associated with a unit in neural networks suggested that the introduction of fuzziness into the activity of the unit would be appropriate. It is demonstrated that the idea of imprecise distinction between excitation and inhibition can be manipulated easily by fuzzy activation functions. A mathematical formulation of fuzzy activation functions, which are generalization of the two-valued interpretation of activation of a unit is presented, and their relations to other different classes of activation functions are discussed. Furthermore, it is shown that fuzzy activation functions have sufficient power to deal with the fuzzy phenomena of the activity of a unit, with the restriction that the behavior is Boolean-like. Examples are given to illustrate the analysis and synthesis of the fuzzy activation function